4x^2+36=32x

Solution for 4x^2+36=32x equation:

4x^2+36=32x

We move all terms to the left:

4x^2+36-(32x)=0

a = 4; b = -32; c = +36;
Δ = b2-4ac
Δ = -322-4·4·36
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8\sqrt{7}}{2*4}=\frac{32-8\sqrt{7}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8\sqrt{7}}{2*4}=\frac{32+8\sqrt{7}}{8}
$