4x^2-32x=-55

Solution for 4x^2-32x=-55 equation:

4x^2-32x=-55

We move all terms to the left:

4x^2-32x-(-55)=0

We add all the numbers together, and all the variables

4x^2-32x+55=0

a = 4; b = -32; c = +55;
Δ = b2-4ac
Δ = -322-4·4·55
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-12}{2*4}=\frac{20}{8}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+12}{2*4}=\frac{44}{8}
=5+1/2
$