Solve 3x^2+5-10=12

$$3 x ^ { 2 } + 5 - 10 = 12$$

Solve for x

$$x = \frac{\sqrt{51}}{3} \approx 2.380476143$$

$$x = -\frac{\sqrt{51}}{3} \approx -2.380476143$$

Steps by Finding Square Root

Subtract 10 from 5 to get -5.

$$3x^{2}-5=12$$

Add 5 to both sides.

$$3x^{2}=12+5$$

Add 12 and 5 to get 17.

$$3x^{2}=17$$

Divide both sides by 3.

$$x^{2}=\frac{17}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{51}}{3} x=-\frac{\sqrt{51}}{3}$$

Steps Using the Quadratic Formula

Subtract 10 from 5 to get -5.

$$3x^{2}-5=12$$

Subtract 12 from both sides.

$$3x^{2}-5-12=0$$

Subtract 12 from -5 to get -17.

$$3x^{2}-17=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -17 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-17\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-17\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-17\right)}}{2\times 3}$$

Multiply -12 times -17.

$$x=\frac{0±\sqrt{204}}{2\times 3}$$

Take the square root of 204.

$$x=\frac{0±2\sqrt{51}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±2\sqrt{51}}{6}$$

Now solve the equation x=\frac{0±2\sqrt{51}}{6} when ± is plus.

$$x=\frac{\sqrt{51}}{3}$$

Now solve the equation x=\frac{0±2\sqrt{51}}{6} when ± is minus.

$$x=-\frac{\sqrt{51}}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{51}}{3} x=-\frac{\sqrt{51}}{3}$$