(w-7)w=260

Solution for (w-7)w=260 equation:

(w-7)w=260

We move all terms to the left:

(w-7)w-(260)=0

We multiply parentheses

w^2-7w-260=0

a = 1; b = -7; c = -260;
Δ = b2-4ac
Δ = -72-4·1·(-260)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-33}{2*1}=\frac{-26}{2}
=-13
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+33}{2*1}=\frac{40}{2}
=20
$