Solve sqrt{102}x^2+y=0

$$\sqrt { 102 } x ^ { 2 } + y = 0$$

Solve for y

$$y=-\sqrt{102}x^{2}$$

Solution Steps

Subtract \sqrt{102}x^{2} from both sides. Anything subtracted from zero gives its negation.

$$y=-\sqrt{102}x^{2}$$

Solve for x (complex solution)

$$x=-\frac{102^{\frac{3}{4}}i\sqrt{y}}{102}$$

$$x=\frac{102^{\frac{3}{4}}i\sqrt{y}}{102}$$

Solve for x

$$x=\frac{102^{\frac{3}{4}}\sqrt{-y}}{102}$$

$$x=-\frac{102^{\frac{3}{4}}\sqrt{-y}}{102}\text{, }y\leq 0$$