4a^2-8a=32

Solution for 4a^2-8a=32 equation:

4a^2-8a=32

We move all terms to the left:

4a^2-8a-(32)=0

a = 4; b = -8; c = -32;
Δ = b2-4ac
Δ = -82-4·4·(-32)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-24}{2*4}=\frac{-16}{8}
=-2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+24}{2*4}=\frac{32}{8}
=4
$