4b+b^2=84

Solution for 4b+b^2=84 equation:

4b+b^2=84

We move all terms to the left:

4b+b^2-(84)=0

a = 1; b = 4; c = -84;
Δ = b2-4ac
Δ = 42-4·1·(-84)
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{22}}{2*1}=\frac{-4-4\sqrt{22}}{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{22}}{2*1}=\frac{-4+4\sqrt{22}}{2}
$