Solve 4*1/3x^2-1+1=45

$$4 \times \frac { 1 } { 3 } x ^ { 2 } - 1 + 1 = 45$$

Solve for x

$$x = \frac{3 \sqrt{15}}{2} \approx 5.809475019$$

$$x = -\frac{3 \sqrt{15}}{2} \approx -5.809475019$$

Steps by Finding Square Root

Multiply 4 and \frac{1}{3} to get \frac{4}{3}.

$$\frac{4}{3}x^{2}-1+1=45$$

Add -1 and 1 to get 0.

$$\frac{4}{3}x^{2}=45$$

Multiply both sides by \frac{3}{4}, the reciprocal of \frac{4}{3}.

$$x^{2}=45\times \frac{3}{4}$$

Multiply 45 and \frac{3}{4} to get \frac{135}{4}.

$$x^{2}=\frac{135}{4}$$

Take the square root of both sides of the equation.

$$x=\frac{3\sqrt{15}}{2} x=-\frac{3\sqrt{15}}{2}$$

Steps Using the Quadratic Formula

Multiply 4 and \frac{1}{3} to get \frac{4}{3}.

$$\frac{4}{3}x^{2}-1+1=45$$

Add -1 and 1 to get 0.

$$\frac{4}{3}x^{2}=45$$

Subtract 45 from both sides.

$$\frac{4}{3}x^{2}-45=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{4}{3} for a, 0 for b, and -45 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{4}{3}\left(-45\right)}}{2\times \frac{4}{3}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{4}{3}\left(-45\right)}}{2\times \frac{4}{3}}$$

Multiply -4 times \frac{4}{3}.

$$x=\frac{0±\sqrt{-\frac{16}{3}\left(-45\right)}}{2\times \frac{4}{3}}$$

Multiply -\frac{16}{3} times -45.

$$x=\frac{0±\sqrt{240}}{2\times \frac{4}{3}}$$

Take the square root of 240.

$$x=\frac{0±4\sqrt{15}}{2\times \frac{4}{3}}$$

Multiply 2 times \frac{4}{3}.

$$x=\frac{0±4\sqrt{15}}{\frac{8}{3}}$$

Now solve the equation x=\frac{0±4\sqrt{15}}{\frac{8}{3}} when ± is plus.

$$x=\frac{3\sqrt{15}}{2}$$

Now solve the equation x=\frac{0±4\sqrt{15}}{\frac{8}{3}} when ± is minus.

$$x=-\frac{3\sqrt{15}}{2}$$

The equation is now solved.

$$x=\frac{3\sqrt{15}}{2} x=-\frac{3\sqrt{15}}{2}$$