Solve 20/9a^2=15

$$\frac { 20 } { 9 } a ^ { 2 } = 15$$

Solve for a

$$a = \frac{3 \sqrt{3}}{2} \approx 2.598076211$$

$$a = -\frac{3 \sqrt{3}}{2} \approx -2.598076211$$

Steps by Finding Square Root

Multiply both sides by \frac{9}{20}, the reciprocal of \frac{20}{9}.

$$a^{2}=15\times \frac{9}{20}$$

Multiply 15 and \frac{9}{20} to get \frac{27}{4}.

$$a^{2}=\frac{27}{4}$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Multiply both sides by \frac{9}{20}, the reciprocal of \frac{20}{9}.

$$a^{2}=15\times \frac{9}{20}$$

Multiply 15 and \frac{9}{20} to get \frac{27}{4}.

$$a^{2}=\frac{27}{4}$$

Subtract \frac{27}{4} from both sides.

$$a^{2}-\frac{27}{4}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{27}{4} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-\frac{27}{4}\right)}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-\frac{27}{4}\right)}}{2}$$

Multiply -4 times -\frac{27}{4}.

$$a=\frac{0±\sqrt{27}}{2}$$

Take the square root of 27.

$$a=\frac{0±3\sqrt{3}}{2}$$

Now solve the equation a=\frac{0±3\sqrt{3}}{2} when ± is plus.

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

Now solve the equation a=\frac{0±3\sqrt{3}}{2} when ± is minus.

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

The equation is now solved.

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