(11w+2)w=63

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

(11w+2)w=63

We move all terms to the left:

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

We multiply parentheses

11w^2+2w-63=0

a = 11; b = 2; c = -63;
Δ = b2-4ac
Δ = 22-4·11·(-63)
Δ = 2776
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:

$\sqrt{\Delta}=\sqrt{2776}=\sqrt{4*694}=\sqrt{4}*\sqrt{694}=2\sqrt{694}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{694}}{2*11}=\frac{-2-2\sqrt{694}}{22}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{694}}{2*11}=\frac{-2+2\sqrt{694}}{22}
$