Solve x(20x-x)div2=50

$$x ( 20 x - x ) \div 2 = 50$$

Solve for x

$$x = \frac{10 \sqrt{19}}{19} \approx 2.294157339$$

$$x = -\frac{10 \sqrt{19}}{19} \approx -2.294157339$$

Steps by Finding Square Root

Multiply both sides by 2.

$$x\left(20x-x\right)=50\times 2$$

Combine 20x and -x to get 19x.

$$x\times 19x=50\times 2$$

Multiply x and x to get x^{2}.

$$x^{2}\times 19=50\times 2$$

Multiply 50 and 2 to get 100.

$$x^{2}\times 19=100$$

Divide both sides by 19.

$$x^{2}=\frac{100}{19}$$

Take the square root of both sides of the equation.

$$x=\frac{10\sqrt{19}}{19} x=-\frac{10\sqrt{19}}{19}$$

Steps Using the Quadratic Formula

Multiply both sides by 2.

$$x\left(20x-x\right)=50\times 2$$

Combine 20x and -x to get 19x.

$$x\times 19x=50\times 2$$

Multiply x and x to get x^{2}.

$$x^{2}\times 19=50\times 2$$

Multiply 50 and 2 to get 100.

$$x^{2}\times 19=100$$

Subtract 100 from both sides.

$$x^{2}\times 19-100=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$19x^{2}-100=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 19 for a, 0 for b, and -100 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 19\left(-100\right)}}{2\times 19}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 19\left(-100\right)}}{2\times 19}$$

Multiply -4 times 19.

$$x=\frac{0±\sqrt{-76\left(-100\right)}}{2\times 19}$$

Multiply -76 times -100.

$$x=\frac{0±\sqrt{7600}}{2\times 19}$$

Take the square root of 7600.

$$x=\frac{0±20\sqrt{19}}{2\times 19}$$

Multiply 2 times 19.

$$x=\frac{0±20\sqrt{19}}{38}$$

Now solve the equation x=\frac{0±20\sqrt{19}}{38} when ± is plus.

$$x=\frac{10\sqrt{19}}{19}$$

Now solve the equation x=\frac{0±20\sqrt{19}}{38} when ± is minus.

$$x=-\frac{10\sqrt{19}}{19}$$

The equation is now solved.

$$x=\frac{10\sqrt{19}}{19} x=-\frac{10\sqrt{19}}{19}$$