5x^2+24x-72=0

Solution for 5x^2+24x-72=0 equation:

5x^2+24x-72=0

a = 5; b = 24; c = -72;
Δ = b2-4ac
Δ = 242-4·5·(-72)
Δ = 2016
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:

$\sqrt{\Delta}=\sqrt{2016}=\sqrt{144*14}=\sqrt{144}*\sqrt{14}=12\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-12\sqrt{14}}{2*5}=\frac{-24-12\sqrt{14}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+12\sqrt{14}}{2*5}=\frac{-24+12\sqrt{14}}{10}
$