Solve 9a^2+20=0

$$9 a ^ { 2 } + 20 = 0$$

Solve for a

$$a=-\frac{2\sqrt{5}i}{3}\approx -0-1.490711985i$$

$$a=\frac{2\sqrt{5}i}{3}\approx 1.490711985i$$

Steps by Finding Square Root

Subtract 20 from both sides. Anything subtracted from zero gives its negation.

$$9a^{2}=-20$$

Divide both sides by 9.

$$a^{2}=-\frac{20}{9}$$

The equation is now solved.

$$a=\frac{2\sqrt{5}i}{3} a=-\frac{2\sqrt{5}i}{3}$$

Steps Using the Quadratic Formula

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.

$$9a^{2}+20=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 9 for a, 0 for b, and 20 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 9\times 20}}{2\times 9}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 9\times 20}}{2\times 9}$$

Multiply -4 times 9.

$$a=\frac{0±\sqrt{-36\times 20}}{2\times 9}$$

Multiply -36 times 20.

$$a=\frac{0±\sqrt{-720}}{2\times 9}$$

Take the square root of -720.

$$a=\frac{0±12\sqrt{5}i}{2\times 9}$$

Multiply 2 times 9.

$$a=\frac{0±12\sqrt{5}i}{18}$$

Now solve the equation a=\frac{0±12\sqrt{5}i}{18} when ± is plus.

$$a=\frac{2\sqrt{5}i}{3}$$

Now solve the equation a=\frac{0±12\sqrt{5}i}{18} when ± is minus.

$$a=-\frac{2\sqrt{5}i}{3}$$

The equation is now solved.

$$a=\frac{2\sqrt{5}i}{3} a=-\frac{2\sqrt{5}i}{3}$$