Solve 3x^2+30=4

$$3 x ^ { 2 } + 30 = 4$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{78}i}{3}\approx -0-2.943920289i$$

$$x=\frac{\sqrt{78}i}{3}\approx 2.943920289i$$

Steps by Finding Square Root

Subtract 30 from both sides.

$$3x^{2}=4-30$$

Subtract 30 from 4 to get -26.

$$3x^{2}=-26$$

Divide both sides by 3.

$$x^{2}=-\frac{26}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{78}i}{3} x=-\frac{\sqrt{78}i}{3}$$

Steps Using the Quadratic Formula

Subtract 4 from both sides.

$$3x^{2}+30-4=0$$

Subtract 4 from 30 to get 26.

$$3x^{2}+26=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and 26 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\times 26}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\times 26}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\times 26}}{2\times 3}$$

Multiply -12 times 26.

$$x=\frac{0±\sqrt{-312}}{2\times 3}$$

Take the square root of -312.

$$x=\frac{0±2\sqrt{78}i}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±2\sqrt{78}i}{6}$$

Now solve the equation x=\frac{0±2\sqrt{78}i}{6} when ± is plus.

$$x=\frac{\sqrt{78}i}{3}$$

Now solve the equation x=\frac{0±2\sqrt{78}i}{6} when ± is minus.

$$x=-\frac{\sqrt{78}i}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{78}i}{3} x=-\frac{\sqrt{78}i}{3}$$