b(b+84)=1824

Solution for b(b+84)=1824 equation:

b(b+84)=1824

We move all terms to the left:

b(b+84)-(1824)=0

We multiply parentheses

b^2+84b-1824=0

a = 1; b = 84; c = -1824;
Δ = b2-4ac
Δ = 842-4·1·(-1824)
Δ = 14352
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:

$\sqrt{\Delta}=\sqrt{14352}=\sqrt{16*897}=\sqrt{16}*\sqrt{897}=4\sqrt{897}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-4\sqrt{897}}{2*1}=\frac{-84-4\sqrt{897}}{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+4\sqrt{897}}{2*1}=\frac{-84+4\sqrt{897}}{2}
$