Solve 75/4+5a/4a=0

$$\frac { 75 } { 4 } + \frac { 5 a } { 4 } a = 0$$

Solve for a

$$a=-\sqrt{15}i\approx -0-3.872983346i$$

$$a=\sqrt{15}i\approx 3.872983346i$$

Steps by Finding Square Root

Multiply both sides of the equation by 4.

$$75+5aa=0$$

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

$$75+5a^{2}=0$$

Subtract 75 from both sides. Anything subtracted from zero gives its negation.

$$5a^{2}=-75$$

Divide both sides by 5.

$$a^{2}=\frac{-75}{5}$$

Divide -75 by 5 to get -15.

$$a^{2}=-15$$

The equation is now solved.

$$a=\sqrt{15}i a=-\sqrt{15}i$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 4.

$$75+5aa=0$$

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

$$75+5a^{2}=0$$

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.

$$5a^{2}+75=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and 75 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 5\times 75}}{2\times 5}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 5\times 75}}{2\times 5}$$

Multiply -4 times 5.

$$a=\frac{0±\sqrt{-20\times 75}}{2\times 5}$$

Multiply -20 times 75.

$$a=\frac{0±\sqrt{-1500}}{2\times 5}$$

Take the square root of -1500.

$$a=\frac{0±10\sqrt{15}i}{2\times 5}$$

Multiply 2 times 5.

$$a=\frac{0±10\sqrt{15}i}{10}$$

Now solve the equation a=\frac{0±10\sqrt{15}i}{10} when ± is plus.

$$a=\sqrt{15}i$$

Now solve the equation a=\frac{0±10\sqrt{15}i}{10} when ± is minus.

$$a=-\sqrt{15}i$$

The equation is now solved.

$$a=\sqrt{15}i a=-\sqrt{15}i$$