Solve 1/2=9y^2/5+15

$$\frac { 1 } { 2 } = \frac { 9 y ^ { 2 } } { 5 } + 15$$

Solve for y

$$y=-\frac{\sqrt{290}i}{6}\approx -0-2.838231061i$$

$$y=\frac{\sqrt{290}i}{6}\approx 2.838231061i$$

Steps by Finding Square Root

Multiply both sides of the equation by 10, the least common multiple of 2,5.

$$5=2\times 9y^{2}+150$$

Multiply 2 and 9 to get 18.

$$5=18y^{2}+150$$

Swap sides so that all variable terms are on the left hand side.

$$18y^{2}+150=5$$

Subtract 150 from both sides.

$$18y^{2}=5-150$$

Subtract 150 from 5 to get -145.

$$18y^{2}=-145$$

Divide both sides by 18.

$$y^{2}=-\frac{145}{18}$$

The equation is now solved.

$$y=\frac{\sqrt{290}i}{6} y=-\frac{\sqrt{290}i}{6}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 10, the least common multiple of 2,5.

$$5=2\times 9y^{2}+150$$

Multiply 2 and 9 to get 18.

$$5=18y^{2}+150$$

Swap sides so that all variable terms are on the left hand side.

$$18y^{2}+150=5$$

Subtract 5 from both sides.

$$18y^{2}+150-5=0$$

Subtract 5 from 150 to get 145.

$$18y^{2}+145=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 18 for a, 0 for b, and 145 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 18\times 145}}{2\times 18}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 18\times 145}}{2\times 18}$$

Multiply -4 times 18.

$$y=\frac{0±\sqrt{-72\times 145}}{2\times 18}$$

Multiply -72 times 145.

$$y=\frac{0±\sqrt{-10440}}{2\times 18}$$

Take the square root of -10440.

$$y=\frac{0±6\sqrt{290}i}{2\times 18}$$

Multiply 2 times 18.

$$y=\frac{0±6\sqrt{290}i}{36}$$

Now solve the equation y=\frac{0±6\sqrt{290}i}{36} when ± is plus.

$$y=\frac{\sqrt{290}i}{6}$$

Now solve the equation y=\frac{0±6\sqrt{290}i}{36} when ± is minus.

$$y=-\frac{\sqrt{290}i}{6}$$

The equation is now solved.

$$y=\frac{\sqrt{290}i}{6} y=-\frac{\sqrt{290}i}{6}$$