Solve 3r^2-10=-48

$$3 r ^ { 2 } - 10 = - 48$$

Solve for r

$$r=-\frac{\sqrt{114}i}{3}\approx -0-3.559026084i$$

$$r=\frac{\sqrt{114}i}{3}\approx 3.559026084i$$

Steps by Finding Square Root

Add 10 to both sides.

$$3r^{2}=-48+10$$

Add -48 and 10 to get -38.

$$3r^{2}=-38$$

Divide both sides by 3.

$$r^{2}=-\frac{38}{3}$$

The equation is now solved.

$$r=\frac{\sqrt{114}i}{3} r=-\frac{\sqrt{114}i}{3}$$

Steps Using the Quadratic Formula

Add 48 to both sides.

$$3r^{2}-10+48=0$$

Add -10 and 48 to get 38.

$$3r^{2}+38=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and 38 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\times 3\times 38}}{2\times 3}$$

Square 0.

$$r=\frac{0±\sqrt{-4\times 3\times 38}}{2\times 3}$$

Multiply -4 times 3.

$$r=\frac{0±\sqrt{-12\times 38}}{2\times 3}$$

Multiply -12 times 38.

$$r=\frac{0±\sqrt{-456}}{2\times 3}$$

Take the square root of -456.

$$r=\frac{0±2\sqrt{114}i}{2\times 3}$$

Multiply 2 times 3.

$$r=\frac{0±2\sqrt{114}i}{6}$$

Now solve the equation r=\frac{0±2\sqrt{114}i}{6} when ± is plus.

$$r=\frac{\sqrt{114}i}{3}$$

Now solve the equation r=\frac{0±2\sqrt{114}i}{6} when ± is minus.

$$r=-\frac{\sqrt{114}i}{3}$$

The equation is now solved.

$$r=\frac{\sqrt{114}i}{3} r=-\frac{\sqrt{114}i}{3}$$