72x^2+270x-81=0

Solution for 72x^2+270x-81=0 equation:

72x^2+270x-81=0

a = 72; b = 270; c = -81;
Δ = b2-4ac
Δ = 2702-4·72·(-81)
Δ = 96228
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:

$\sqrt{\Delta}=\sqrt{96228}=\sqrt{2916*33}=\sqrt{2916}*\sqrt{33}=54\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(270)-54\sqrt{33}}{2*72}=\frac{-270-54\sqrt{33}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(270)+54\sqrt{33}}{2*72}=\frac{-270+54\sqrt{33}}{144}
$