11x^2+6x-12=0

Solution for 11x^2+6x-12=0 equation:

11x^2+6x-12=0

a = 11; b = 6; c = -12;
Δ = b2-4ac
Δ = 62-4·11·(-12)
Δ = 564
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:

$\sqrt{\Delta}=\sqrt{564}=\sqrt{4*141}=\sqrt{4}*\sqrt{141}=2\sqrt{141}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{141}}{2*11}=\frac{-6-2\sqrt{141}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{141}}{2*11}=\frac{-6+2\sqrt{141}}{22}
$