Solve x^2-25x/3x-10=0

$$x ^ { 2 } - \frac { 25 x } { 3 } x - 10 = 0$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{165}i}{11}\approx -0-1.167748416i$$

$$x=\frac{\sqrt{165}i}{11}\approx 1.167748416i$$

Steps by Finding Square Root

Multiply both sides of the equation by 3.

$$3\left(x^{2}-\frac{25x}{3}x\right)-30=0$$

Express \frac{25x}{3}x as a single fraction.

$$3\left(x^{2}-\frac{25xx}{3}\right)-30=0$$

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

$$3\left(x^{2}-\frac{25x^{2}}{3}\right)-30=0$$

Use the distributive property to multiply 3 by x^{2}-\frac{25x^{2}}{3}.

$$3x^{2}+3\left(-\frac{25x^{2}}{3}\right)-30=0$$

Express 3\left(-\frac{25x^{2}}{3}\right) as a single fraction.

$$3x^{2}+\frac{-3\times 25x^{2}}{3}-30=0$$

Cancel out 3 and 3.

$$3x^{2}-25x^{2}-30=0$$

Combine 3x^{2} and -25x^{2} to get -22x^{2}.

$$-22x^{2}-30=0$$

Add 30 to both sides. Anything plus zero gives itself.

$$-22x^{2}=30$$

Divide both sides by -22.

$$x^{2}=\frac{30}{-22}$$

Reduce the fraction \frac{30}{-22} to lowest terms by extracting and canceling out 2.

$$x^{2}=-\frac{15}{11}$$

The equation is now solved.

$$x=\frac{\sqrt{165}i}{11} x=-\frac{\sqrt{165}i}{11}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 3.

$$3\left(x^{2}-\frac{25x}{3}x\right)-30=0$$

Express \frac{25x}{3}x as a single fraction.

$$3\left(x^{2}-\frac{25xx}{3}\right)-30=0$$

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

$$3\left(x^{2}-\frac{25x^{2}}{3}\right)-30=0$$

Use the distributive property to multiply 3 by x^{2}-\frac{25x^{2}}{3}.

$$3x^{2}+3\left(-\frac{25x^{2}}{3}\right)-30=0$$

Express 3\left(-\frac{25x^{2}}{3}\right) as a single fraction.

$$3x^{2}+\frac{-3\times 25x^{2}}{3}-30=0$$

Cancel out 3 and 3.

$$3x^{2}-25x^{2}-30=0$$

Combine 3x^{2} and -25x^{2} to get -22x^{2}.

$$-22x^{2}-30=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -22 for a, 0 for b, and -30 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-22\right)\left(-30\right)}}{2\left(-22\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-22\right)\left(-30\right)}}{2\left(-22\right)}$$

Multiply -4 times -22.

$$x=\frac{0±\sqrt{88\left(-30\right)}}{2\left(-22\right)}$$

Multiply 88 times -30.

$$x=\frac{0±\sqrt{-2640}}{2\left(-22\right)}$$

Take the square root of -2640.

$$x=\frac{0±4\sqrt{165}i}{2\left(-22\right)}$$

Multiply 2 times -22.

$$x=\frac{0±4\sqrt{165}i}{-44}$$

Now solve the equation x=\frac{0±4\sqrt{165}i}{-44} when ± is plus.

$$x=-\frac{\sqrt{165}i}{11}$$

Now solve the equation x=\frac{0±4\sqrt{165}i}{-44} when ± is minus.

$$x=\frac{\sqrt{165}i}{11}$$

The equation is now solved.

$$x=-\frac{\sqrt{165}i}{11} x=\frac{\sqrt{165}i}{11}$$