w^2+24w-40=0

Solution for w^2+24w-40=0 equation:

w^2+24w-40=0

a = 1; b = 24; c = -40;
Δ = b2-4ac
Δ = 242-4·1·(-40)
Δ = 736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{46}}{2*1}=\frac{-24-4\sqrt{46}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{46}}{2*1}=\frac{-24+4\sqrt{46}}{2}
$