5x^2-13=11

Solution for 5x^2-13=11 equation:

5x^2-13=11

We move all terms to the left:

5x^2-13-(11)=0

We add all the numbers together, and all the variables

5x^2-24=0

a = 5; b = 0; c = -24;
Δ = b2-4ac
Δ = 02-4·5·(-24)
Δ = 480
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{30}}{2*5}=\frac{0-4\sqrt{30}}{10}
=-\frac{4\sqrt{30}}{10}
=-\frac{2\sqrt{30}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{30}}{2*5}=\frac{0+4\sqrt{30}}{10}
=\frac{4\sqrt{30}}{10}
=\frac{2\sqrt{30}}{5}
$