11x^2+12x-144=0

Solution for 11x^2+12x-144=0 equation:

11x^2+12x-144=0

a = 11; b = 12; c = -144;
Δ = b2-4ac
Δ = 122-4·11·(-144)
Δ = 6480
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:

$\sqrt{\Delta}=\sqrt{6480}=\sqrt{1296*5}=\sqrt{1296}*\sqrt{5}=36\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-36\sqrt{5}}{2*11}=\frac{-12-36\sqrt{5}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+36\sqrt{5}}{2*11}=\frac{-12+36\sqrt{5}}{22}
$