(2w+11)(w)=63

Solution for (2w+11)(w)=63 equation:

(2w+11)(w)=63

We move all terms to the left:

(2w+11)(w)-(63)=0

We multiply parentheses

2w^2+11w-63=0

a = 2; b = 11; c = -63;
Δ = b2-4ac
Δ = 112-4·2·(-63)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-25}{2*2}=\frac{-36}{4}
=-9
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+25}{2*2}=\frac{14}{4}
=3+1/2
$