b^2-76b-1440=0

Solution for b^2-76b-1440=0 equation:

b^2-76b-1440=0

a = 1; b = -76; c = -1440;
Δ = b2-4ac
Δ = -762-4·1·(-1440)
Δ = 11536
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:

$\sqrt{\Delta}=\sqrt{11536}=\sqrt{16*721}=\sqrt{16}*\sqrt{721}=4\sqrt{721}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-4\sqrt{721}}{2*1}=\frac{76-4\sqrt{721}}{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+4\sqrt{721}}{2*1}=\frac{76+4\sqrt{721}}{2}
$