Solve 7x^2-5x^2+24=0

$$7 { x }^{ 2 } -5 { x }^{ 2 } +24=0$$

Solve for x (complex solution)

$$x=-2\sqrt{3}i\approx -0-3.464101615i$$

$$x=2\sqrt{3}i\approx 3.464101615i$$

Steps by Finding Square Root

Combine 7x^{2} and -5x^{2} to get 2x^{2}.

$$2x^{2}+24=0$$

Subtract 24 from both sides. Anything subtracted from zero gives its negation.

$$2x^{2}=-24$$

Divide both sides by 2.

$$x^{2}=\frac{-24}{2}$$

Divide -24 by 2 to get -12.

$$x^{2}=-12$$

The equation is now solved.

$$x=2\sqrt{3}i x=-2\sqrt{3}i$$

Steps Using the Quadratic Formula

Combine 7x^{2} and -5x^{2} to get 2x^{2}.

$$2x^{2}+24=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and 24 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\times 24}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\times 24}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\times 24}}{2\times 2}$$

Multiply -8 times 24.

$$x=\frac{0±\sqrt{-192}}{2\times 2}$$

Take the square root of -192.

$$x=\frac{0±8\sqrt{3}i}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±8\sqrt{3}i}{4}$$

Now solve the equation x=\frac{0±8\sqrt{3}i}{4} when ± is plus.

$$x=2\sqrt{3}i$$

Now solve the equation x=\frac{0±8\sqrt{3}i}{4} when ± is minus.

$$x=-2\sqrt{3}i$$

The equation is now solved.

$$x=2\sqrt{3}i x=-2\sqrt{3}i$$