4b^2+32b=57

Solution for 4b^2+32b=57 equation:

4b^2+32b=57

We move all terms to the left:

4b^2+32b-(57)=0

a = 4; b = 32; c = -57;
Δ = b2-4ac
Δ = 322-4·4·(-57)
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-44}{2*4}=\frac{-76}{8}
=-9+1/2
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+44}{2*4}=\frac{12}{8}
=1+1/2
$