Solve (1215-x)*30000+30000=36790/x

$$( 1215 - x ) \times 30000 + 30000 = \frac { 36790 } { x }$$

Solve for x

$$x=\frac{\sqrt{33269649630}}{300}+608\approx 1215.998991501$$

$$x=-\frac{\sqrt{33269649630}}{300}+608\approx 0.001008499$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$\left(1215-x\right)\times 30000x+x\times 30000=36790$$

Use the distributive property to multiply 1215-x by 30000.

$$\left(36450000-30000x\right)x+x\times 30000=36790$$

Use the distributive property to multiply 36450000-30000x by x.

$$36450000x-30000x^{2}+x\times 30000=36790$$

Combine 36450000x and x\times 30000 to get 36480000x.

$$36480000x-30000x^{2}=36790$$

Subtract 36790 from both sides.

$$36480000x-30000x^{2}-36790=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$-30000x^{2}[phone]x-36790=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -30000 for a, 36480000 for b, and -36790 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-36480000±\sqrt{36480000^{2}-4\left(-30000\right)\left(-36790\right)}}{2\left(-30000\right)}$$

Square 36480000.

$$x=\frac{-36480000±\sqrt{1330790400000000-4\left(-30000\right)\left(-36790\right)}}{2\left(-30000\right)}$$

Multiply -4 times -30000.

$$x=\frac{-36480000±\sqrt{1330790400000000+120000\left(-36790\right)}}{2\left(-30000\right)}$$

Multiply 120000 times -36790.

$$x=\frac{-36480000±\sqrt{1330790400000000-4414800000}}{2\left(-30000\right)}$$

Add 1330790400000000 to -4414800000.

$$x=\frac{-36480000±\sqrt{1330785985200000}}{2\left(-30000\right)}$$

Take the square root of 1330785985200000.

$$x=\frac{-36480000±200\sqrt{33269649630}}{2\left(-30000\right)}$$

Multiply 2 times -30000.

$$x=\frac{-36480000±200\sqrt{33269649630}}{-60000}$$

Now solve the equation x=\frac{-36480000±200\sqrt{33269649630}}{-60000} when ± is plus. Add -36480000 to 200\sqrt{33269649630}.

$$x=\frac{200\sqrt{33269649630}-36480000}{-60000}$$

Divide -36480000+200\sqrt{33269649630} by -60000.

$$x=-\frac{\sqrt{33269649630}}{300}+608$$

Now solve the equation x=\frac{-36480000±200\sqrt{33269649630}}{-60000} when ± is minus. Subtract 200\sqrt{33269649630} from -36480000.

$$x=\frac{-200\sqrt{33269649630}-36480000}{-60000}$$

Divide -36480000-200\sqrt{33269649630} by -60000.

$$x=\frac{\sqrt{33269649630}}{300}+608$$

The equation is now solved.

$$x=-\frac{\sqrt{33269649630}}{300}+608 x=\frac{\sqrt{33269649630}}{300}+608$$

Steps for Completing the Square

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$\left(1215-x\right)\times 30000x+x\times 30000=36790$$

Use the distributive property to multiply 1215-x by 30000.

$$\left(36450000-30000x\right)x+x\times 30000=36790$$

Use the distributive property to multiply 36450000-30000x by x.

$$36450000x-30000x^{2}+x\times 30000=36790$$

Combine 36450000x and x\times 30000 to get 36480000x.

$$36480000x-30000x^{2}=36790$$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$-30000x^{2}[phone]x=36790$$

Divide both sides by -30000.

$$\frac{-30000x^{2}[phone]x}{-30000}=\frac{36790}{-30000}$$

Dividing by -30000 undoes the multiplication by -30000.

$$x^{2}+\frac{36480000}{-30000}x=\frac{36790}{-30000}$$

Divide 36480000 by -30000.

$$x^{2}-1216x=\frac{36790}{-30000}$$

Reduce the fraction \frac{36790}{-30000} to lowest terms by extracting and canceling out 10.

$$x^{2}-1216x=-\frac{3679}{3000}$$

Divide -1216, the coefficient of the x term, by 2 to get -608. Then add the square of -608 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-1216x+\left(-608\right)^{2}=-\frac{3679}{3000}+\left(-608\right)^{2}$$

Square -608.

$$x^{2}-1216x+369664=-\frac{3679}{3000}+369664$$

Add -\frac{3679}{3000} to 369664.

$$x^{2}-1216x+369664=\frac{1108988321}{3000}$$

Factor x^{2}-1216x+369664. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-608\right)^{2}=\frac{1108988321}{3000}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-608\right)^{2}}=\sqrt{\frac{1108988321}{3000}}$$

Simplify.

$$x-608=\frac{\sqrt{33269649630}}{300} x-608=-\frac{\sqrt{33269649630}}{300}$$

Add 608 to both sides of the equation.

$$x=\frac{\sqrt{33269649630}}{300}+608 x=-\frac{\sqrt{33269649630}}{300}+608$$