Solve 3x^2+5=40

$$3 x ^ { 2 } + 5 = 40$$

Solve for x

$$x = \frac{\sqrt{105}}{3} \approx 3.415650255$$

$$x = -\frac{\sqrt{105}}{3} \approx -3.415650255$$

Steps by Finding Square Root

Subtract 5 from both sides.

$$3x^{2}=40-5$$

Subtract 5 from 40 to get 35.

$$3x^{2}=35$$

Divide both sides by 3.

$$x^{2}=\frac{35}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{105}}{3} x=-\frac{\sqrt{105}}{3}$$

Steps Using the Quadratic Formula

Subtract 40 from both sides.

$$3x^{2}+5-40=0$$

Subtract 40 from 5 to get -35.

$$3x^{2}-35=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -35 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-35\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-35\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-35\right)}}{2\times 3}$$

Multiply -12 times -35.

$$x=\frac{0±\sqrt{420}}{2\times 3}$$

Take the square root of 420.

$$x=\frac{0±2\sqrt{105}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±2\sqrt{105}}{6}$$

Now solve the equation x=\frac{0±2\sqrt{105}}{6} when ± is plus.

$$x=\frac{\sqrt{105}}{3}$$

Now solve the equation x=\frac{0±2\sqrt{105}}{6} when ± is minus.

$$x=-\frac{\sqrt{105}}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{105}}{3} x=-\frac{\sqrt{105}}{3}$$