(w+6)w=130

Solution for (w+6)w=130 equation:

(w+6)w=130

We move all terms to the left:

(w+6)w-(130)=0

We multiply parentheses

w^2+6w-130=0

a = 1; b = 6; c = -130;
Δ = b2-4ac
Δ = 62-4·1·(-130)
Δ = 556
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:

$\sqrt{\Delta}=\sqrt{556}=\sqrt{4*139}=\sqrt{4}*\sqrt{139}=2\sqrt{139}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{139}}{2*1}=\frac{-6-2\sqrt{139}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{139}}{2*1}=\frac{-6+2\sqrt{139}}{2}
$