4b^2-4b-112=0

Solution for 4b^2-4b-112=0 equation:

4b^2-4b-112=0

a = 4; b = -4; c = -112;
Δ = b2-4ac
Δ = -42-4·4·(-112)
Δ = 1808
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1808}=\sqrt{16*113}=\sqrt{16}*\sqrt{113}=4\sqrt{113}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{113}}{2*4}=\frac{4-4\sqrt{113}}{8}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{113}}{2*4}=\frac{4+4\sqrt{113}}{8}
$