72x^2+2x-1152=0

Solution for 72x^2+2x-1152=0 equation:

72x^2+2x-1152=0

a = 72; b = 2; c = -1152;
Δ = b2-4ac
Δ = 22-4·72·(-1152)
Δ = 331780
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:

$\sqrt{\Delta}=\sqrt{331780}=\sqrt{4*82945}=\sqrt{4}*\sqrt{82945}=2\sqrt{82945}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{82945}}{2*72}=\frac{-2-2\sqrt{82945}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{82945}}{2*72}=\frac{-2+2\sqrt{82945}}{144}
$