Solve 6a^2-3=4

$$6 a ^ { 2 } - 3 = 4$$

Solve for a

$$a = \frac{\sqrt{42}}{6} \approx 1.08012345$$

$$a = -\frac{\sqrt{42}}{6} \approx -1.08012345$$

Steps by Finding Square Root

Add 3 to both sides.

$$6a^{2}=4+3$$

Add 4 and 3 to get 7.

$$6a^{2}=7$$

Divide both sides by 6.

$$a^{2}=\frac{7}{6}$$

Take the square root of both sides of the equation.

$$a=\frac{\sqrt{42}}{6} a=-\frac{\sqrt{42}}{6}$$

Steps Using the Quadratic Formula

Subtract 4 from both sides.

$$6a^{2}-3-4=0$$

Subtract 4 from -3 to get -7.

$$6a^{2}-7=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 0 for b, and -7 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 6\left(-7\right)}}{2\times 6}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 6\left(-7\right)}}{2\times 6}$$

Multiply -4 times 6.

$$a=\frac{0±\sqrt{-24\left(-7\right)}}{2\times 6}$$

Multiply -24 times -7.

$$a=\frac{0±\sqrt{168}}{2\times 6}$$

Take the square root of 168.

$$a=\frac{0±2\sqrt{42}}{2\times 6}$$

Multiply 2 times 6.

$$a=\frac{0±2\sqrt{42}}{12}$$

Now solve the equation a=\frac{0±2\sqrt{42}}{12} when ± is plus.

$$a=\frac{\sqrt{42}}{6}$$

Now solve the equation a=\frac{0±2\sqrt{42}}{12} when ± is minus.

$$a=-\frac{\sqrt{42}}{6}$$

The equation is now solved.

$$a=\frac{\sqrt{42}}{6} a=-\frac{\sqrt{42}}{6}$$