Solve x-5/3*2x/7=3

$$\frac { x - 5 } { 3 } \times \frac { 2 x } { 7 } = 3$$

Solve for x

$$x = \frac{\sqrt{151} + 5}{2} \approx 8.644102864$$

$$x=\frac{5-\sqrt{151}}{2}\approx -3.644102864$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 21, the least common multiple of 3,7.

$$\left(x-5\right)\times 2x=63$$

Use the distributive property to multiply x-5 by 2.

$$\left(2x-10\right)x=63$$

Use the distributive property to multiply 2x-10 by x.

$$2x^{2}-10x=63$$

Subtract 63 from both sides.

$$2x^{2}-10x-63=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, -10 for b, and -63 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\times 2\left(-63\right)}}{2\times 2}$$

Square -10.

$$x=\frac{-\left(-10\right)±\sqrt{100-4\times 2\left(-63\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{-\left(-10\right)±\sqrt{100-8\left(-63\right)}}{2\times 2}$$

Multiply -8 times -63.

$$x=\frac{-\left(-10\right)±\sqrt{100+504}}{2\times 2}$$

Add 100 to 504.

$$x=\frac{-\left(-10\right)±\sqrt{604}}{2\times 2}$$

Take the square root of 604.

$$x=\frac{-\left(-10\right)±2\sqrt{151}}{2\times 2}$$

The opposite of -10 is 10.

$$x=\frac{10±2\sqrt{151}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{10±2\sqrt{151}}{4}$$

Now solve the equation x=\frac{10±2\sqrt{151}}{4} when ± is plus. Add 10 to 2\sqrt{151}.

$$x=\frac{2\sqrt{151}+10}{4}$$

Divide 10+2\sqrt{151} by 4.

$$x=\frac{\sqrt{151}+5}{2}$$

Now solve the equation x=\frac{10±2\sqrt{151}}{4} when ± is minus. Subtract 2\sqrt{151} from 10.

$$x=\frac{10-2\sqrt{151}}{4}$$

Divide 10-2\sqrt{151} by 4.

$$x=\frac{5-\sqrt{151}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{151}+5}{2} x=\frac{5-\sqrt{151}}{2}$$

Steps for Completing the Square

Multiply both sides of the equation by 21, the least common multiple of 3,7.

$$\left(x-5\right)\times 2x=63$$

Use the distributive property to multiply x-5 by 2.

$$\left(2x-10\right)x=63$$

Use the distributive property to multiply 2x-10 by x.

$$2x^{2}-10x=63$$

Divide both sides by 2.

$$\frac{2x^{2}-10x}{2}=\frac{63}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x^{2}+\left(-\frac{10}{2}\right)x=\frac{63}{2}$$

Divide -10 by 2.

$$x^{2}-5x=\frac{63}{2}$$

Divide -5, the coefficient of the x term, by 2 to get -\frac{5}{2}. Then add the square of -\frac{5}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-5x+\left(-\frac{5}{2}\right)^{2}=\frac{63}{2}+\left(-\frac{5}{2}\right)^{2}$$

Square -\frac{5}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-5x+\frac{25}{4}=\frac{63}{2}+\frac{25}{4}$$

Add \frac{63}{2} to \frac{25}{4} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}-5x+\frac{25}{4}=\frac{151}{4}$$

Factor x^{2}-5x+\frac{25}{4}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{5}{2}\right)^{2}=\frac{151}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{5}{2}\right)^{2}}=\sqrt{\frac{151}{4}}$$

Simplify.

$$x-\frac{5}{2}=\frac{\sqrt{151}}{2} x-\frac{5}{2}=-\frac{\sqrt{151}}{2}$$

Add \frac{5}{2} to both sides of the equation.

$$x=\frac{\sqrt{151}+5}{2} x=\frac{5-\sqrt{151}}{2}$$