4x^2-32x=216

Solution for 4x^2-32x=216 equation:

4x^2-32x=216

We move all terms to the left:

4x^2-32x-(216)=0

a = 4; b = -32; c = -216;
Δ = b2-4ac
Δ = -322-4·4·(-216)
Δ = 4480
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:

$\sqrt{\Delta}=\sqrt{4480}=\sqrt{64*70}=\sqrt{64}*\sqrt{70}=8\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8\sqrt{70}}{2*4}=\frac{32-8\sqrt{70}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8\sqrt{70}}{2*4}=\frac{32+8\sqrt{70}}{8}
$