(w+5)w=76

Solution for (w+5)w=76 equation:

(w+5)w=76

We move all terms to the left:

(w+5)w-(76)=0

We multiply parentheses

w^2+5w-76=0

a = 1; b = 5; c = -76;
Δ = b2-4ac
Δ = 52-4·1·(-76)
Δ = 329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{329}}{2*1}=\frac{-5-\sqrt{329}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{329}}{2*1}=\frac{-5+\sqrt{329}}{2}
$