72x^2+12x-72=0

Solution for 72x^2+12x-72=0 equation:

72x^2+12x-72=0

a = 72; b = 12; c = -72;
Δ = b2-4ac
Δ = 122-4·72·(-72)
Δ = 20880
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:

$\sqrt{\Delta}=\sqrt{20880}=\sqrt{144*145}=\sqrt{144}*\sqrt{145}=12\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{145}}{2*72}=\frac{-12-12\sqrt{145}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{145}}{2*72}=\frac{-12+12\sqrt{145}}{144}
$