11x^2+12x=24

Solution for 11x^2+12x=24 equation:

11x^2+12x=24

We move all terms to the left:

11x^2+12x-(24)=0

a = 11; b = 12; c = -24;
Δ = b2-4ac
Δ = 122-4·11·(-24)
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-20\sqrt{3}}{2*11}=\frac{-12-20\sqrt{3}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+20\sqrt{3}}{2*11}=\frac{-12+20\sqrt{3}}{22}
$