5x^2+36x-24=0

Solution for 5x^2+36x-24=0 equation:

5x^2+36x-24=0

a = 5; b = 36; c = -24;
Δ = b2-4ac
Δ = 362-4·5·(-24)
Δ = 1776
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:

$\sqrt{\Delta}=\sqrt{1776}=\sqrt{16*111}=\sqrt{16}*\sqrt{111}=4\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{111}}{2*5}=\frac{-36-4\sqrt{111}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{111}}{2*5}=\frac{-36+4\sqrt{111}}{10}
$