Solve 5/4x^2-10x^2/3-25=0

$$\frac { 5 } { 4 } x ^ { 2 } - \frac { 10 x ^ { 2 } } { 3 } - 25 = 0$$

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

Multiply both sides of the equation by 12, the least common multiple of 4,3.

$$15x^{2}-4\times 10x^{2}-300=0$$

Multiply -4 and 10 to get -40.

$$15x^{2}-40x^{2}-300=0$$

Combine 15x^{2} and -40x^{2} to get -25x^{2}.

$$-25x^{2}-300=0$$

Add 300 to both sides. Anything plus zero gives itself.

$$-25x^{2}=300$$

Divide both sides by -25.

$$x^{2}=\frac{300}{-25}$$

Divide 300 by -25 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

Multiply both sides of the equation by 12, the least common multiple of 4,3.

$$15x^{2}-4\times 10x^{2}-300=0$$

Multiply -4 and 10 to get -40.

$$15x^{2}-40x^{2}-300=0$$

Combine 15x^{2} and -40x^{2} to get -25x^{2}.

$$-25x^{2}-300=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -25 for a, 0 for b, and -300 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-25\right)\left(-300\right)}}{2\left(-25\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-25\right)\left(-300\right)}}{2\left(-25\right)}$$

Multiply -4 times -25.

$$x=\frac{0±\sqrt{100\left(-300\right)}}{2\left(-25\right)}$$

Multiply 100 times -300.

$$x=\frac{0±\sqrt{-30000}}{2\left(-25\right)}$$

Take the square root of -30000.

$$x=\frac{0±100\sqrt{3}i}{2\left(-25\right)}$$

Multiply 2 times -25.

$$x=\frac{0±100\sqrt{3}i}{-50}$$

Now solve the equation x=\frac{0±100\sqrt{3}i}{-50} when ± is plus.

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

Now solve the equation x=\frac{0±100\sqrt{3}i}{-50} when ± is minus.

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

The equation is now solved.

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