4x^2+32x=11

Solution for 4x^2+32x=11 equation:

4x^2+32x=11

We move all terms to the left:

4x^2+32x-(11)=0

a = 4; b = 32; c = -11;
Δ = b2-4ac
Δ = 322-4·4·(-11)
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{-(32)-20\sqrt{3}}{2*4}=\frac{-32-20\sqrt{3}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+20\sqrt{3}}{2*4}=\frac{-32+20\sqrt{3}}{8}
$