Solve 5x^2+0x-13=0

$$5 { x }^{ 2 } +0x-13=0$$

Solve for x

$$x = \frac{\sqrt{65}}{5} \approx 1.61245155$$

$$x = -\frac{\sqrt{65}}{5} \approx -1.61245155$$

Steps Using the Quadratic Formula

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$5x^{2}-13=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -13 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-13\right)}}{2\times 5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5\left(-13\right)}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\left(-13\right)}}{2\times 5}$$

Multiply -20 times -13.

$$x=\frac{0±\sqrt{260}}{2\times 5}$$

Take the square root of 260.

$$x=\frac{0±2\sqrt{65}}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±2\sqrt{65}}{10}$$

Now solve the equation x=\frac{0±2\sqrt{65}}{10} when ± is plus.

$$x=\frac{\sqrt{65}}{5}$$

Now solve the equation x=\frac{0±2\sqrt{65}}{10} when ± is minus.

$$x=-\frac{\sqrt{65}}{5}$$

The equation is now solved.

$$x=\frac{\sqrt{65}}{5} x=-\frac{\sqrt{65}}{5}$$