Solve (x+2)(x-5)=4x^2-3x

$$( x + 2 ) ( x - 5 ) = 4 x ^ { 2 } - 3 x$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{30}i}{3}\approx -0-1.825741858i$$

$$x=\frac{\sqrt{30}i}{3}\approx 1.825741858i$$

Steps by Finding Square Root

Use the distributive property to multiply x+2 by x-5 and combine like terms.

$$x^{2}-3x-10=4x^{2}-3x$$

Subtract 4x^{2} from both sides.

$$x^{2}-3x-10-4x^{2}=-3x$$

Combine x^{2} and -4x^{2} to get -3x^{2}.

$$-3x^{2}-3x-10=-3x$$

Add 3x to both sides.

$$-3x^{2}-3x-10+3x=0$$

Combine -3x and 3x to get 0.

$$-3x^{2}-10=0$$

Add 10 to both sides. Anything plus zero gives itself.

$$-3x^{2}=10$$

Divide both sides by -3.

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

The equation is now solved.

$$x=\frac{\sqrt{30}i}{3} x=-\frac{\sqrt{30}i}{3}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x+2 by x-5 and combine like terms.

$$x^{2}-3x-10=4x^{2}-3x$$

Subtract 4x^{2} from both sides.

$$x^{2}-3x-10-4x^{2}=-3x$$

Combine x^{2} and -4x^{2} to get -3x^{2}.

$$-3x^{2}-3x-10=-3x$$

Add 3x to both sides.

$$-3x^{2}-3x-10+3x=0$$

Combine -3x and 3x to get 0.

$$-3x^{2}-10=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -3 for a, 0 for b, and -10 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-3\right)\left(-10\right)}}{2\left(-3\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-3\right)\left(-10\right)}}{2\left(-3\right)}$$

Multiply -4 times -3.

$$x=\frac{0±\sqrt{12\left(-10\right)}}{2\left(-3\right)}$$

Multiply 12 times -10.

$$x=\frac{0±\sqrt{-120}}{2\left(-3\right)}$$

Take the square root of -120.

$$x=\frac{0±2\sqrt{30}i}{2\left(-3\right)}$$

Multiply 2 times -3.

$$x=\frac{0±2\sqrt{30}i}{-6}$$

Now solve the equation x=\frac{0±2\sqrt{30}i}{-6} when ± is plus.

$$x=-\frac{\sqrt{30}i}{3}$$

Now solve the equation x=\frac{0±2\sqrt{30}i}{-6} when ± is minus.

$$x=\frac{\sqrt{30}i}{3}$$

The equation is now solved.

$$x=-\frac{\sqrt{30}i}{3} x=\frac{\sqrt{30}i}{3}$$