Solve 15/4x^2-9/20=2.3

$$\frac{ 15 }{ 4 } { x }^{ 2 } - \frac{ 9 }{ 20 } =2.3$$

Solve for x

$$x=\frac{\sqrt{165}}{15}\approx 0.856348839$$

$$x=-\frac{\sqrt{165}}{15}\approx -0.856348839$$

Steps by Finding Square Root

Add \frac{9}{20} to both sides.

$$\frac{15}{4}x^{2}=2.3+\frac{9}{20}$$

Add 2.3 and \frac{9}{20} to get \frac{11}{4}.

$$\frac{15}{4}x^{2}=\frac{11}{4}$$

Multiply both sides by \frac{4}{15}, the reciprocal of \frac{15}{4}.

$$x^{2}=\frac{11}{4}\times \frac{4}{15}$$

Multiply \frac{11}{4} and \frac{4}{15} to get \frac{11}{15}.

$$x^{2}=\frac{11}{15}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{165}}{15} x=-\frac{\sqrt{165}}{15}$$

Steps Using the Quadratic Formula

Subtract 2.3 from both sides.

$$\frac{15}{4}x^{2}-\frac{9}{20}-2.3=0$$

Subtract 2.3 from -\frac{9}{20} to get -\frac{11}{4}.

$$\frac{15}{4}x^{2}-\frac{11}{4}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{15}{4} for a, 0 for b, and -\frac{11}{4} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{15}{4}\left(-\frac{11}{4}\right)}}{2\times \frac{15}{4}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{15}{4}\left(-\frac{11}{4}\right)}}{2\times \frac{15}{4}}$$

Multiply -4 times \frac{15}{4}.

$$x=\frac{0±\sqrt{-15\left(-\frac{11}{4}\right)}}{2\times \frac{15}{4}}$$

Multiply -15 times -\frac{11}{4}.

$$x=\frac{0±\sqrt{\frac{165}{4}}}{2\times \frac{15}{4}}$$

Take the square root of \frac{165}{4}.

$$x=\frac{0±\frac{\sqrt{165}}{2}}{2\times \frac{15}{4}}$$

Multiply 2 times \frac{15}{4}.

$$x=\frac{0±\frac{\sqrt{165}}{2}}{\frac{15}{2}}$$

Now solve the equation x=\frac{0±\frac{\sqrt{165}}{2}}{\frac{15}{2}} when ± is plus.

$$x=\frac{\sqrt{165}}{15}$$

Now solve the equation x=\frac{0±\frac{\sqrt{165}}{2}}{\frac{15}{2}} when ± is minus.

$$x=-\frac{\sqrt{165}}{15}$$

The equation is now solved.

$$x=\frac{\sqrt{165}}{15} x=-\frac{\sqrt{165}}{15}$$