Solve 7x^2+3=6

$$7 x ^ { 2 } + 3 = 6$$

Solve for x

$$x=\frac{\sqrt{21}}{7}\approx 0.654653671$$

$$x=-\frac{\sqrt{21}}{7}\approx -0.654653671$$

Steps by Finding Square Root

Subtract 3 from both sides.

$$7x^{2}=6-3$$

Subtract 3 from 6 to get 3.

$$7x^{2}=3$$

Divide both sides by 7.

$$x^{2}=\frac{3}{7}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{21}}{7} x=-\frac{\sqrt{21}}{7}$$

Steps Using the Quadratic Formula

Subtract 6 from both sides.

$$7x^{2}+3-6=0$$

Subtract 6 from 3 to get -3.

$$7x^{2}-3=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 7 for a, 0 for b, and -3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 7\left(-3\right)}}{2\times 7}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 7\left(-3\right)}}{2\times 7}$$

Multiply -4 times 7.

$$x=\frac{0±\sqrt{-28\left(-3\right)}}{2\times 7}$$

Multiply -28 times -3.

$$x=\frac{0±\sqrt{84}}{2\times 7}$$

Take the square root of 84.

$$x=\frac{0±2\sqrt{21}}{2\times 7}$$

Multiply 2 times 7.

$$x=\frac{0±2\sqrt{21}}{14}$$

Now solve the equation x=\frac{0±2\sqrt{21}}{14} when ± is plus.

$$x=\frac{\sqrt{21}}{7}$$

Now solve the equation x=\frac{0±2\sqrt{21}}{14} when ± is minus.

$$x=-\frac{\sqrt{21}}{7}$$

The equation is now solved.

$$x=\frac{\sqrt{21}}{7} x=-\frac{\sqrt{21}}{7}$$