-4x2=24x+11

Solution for -4x2=24x+11 equation:

-4x^2=24x+11

We move all terms to the left:

-4x^2-(24x+11)=0

We get rid of parentheses

-4x^2-24x-11=0

a = -4; b = -24; c = -11;
Δ = b2-4ac
Δ = -242-4·(-4)·(-11)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-20}{2*-4}=\frac{4}{-8}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+20}{2*-4}=\frac{44}{-8}
=-5+1/2
$