(5+2w)w=63

Solution for (5+2w)w=63 equation:

(5+2w)w=63

We move all terms to the left:

(5+2w)w-(63)=0

We add all the numbers together, and all the variables

(2w+5)w-63=0

We multiply parentheses

2w^2+5w-63=0

a = 2; b = 5; c = -63;
Δ = b2-4ac
Δ = 52-4·2·(-63)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-23}{2*2}=\frac{-28}{4}
=-7
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+23}{2*2}=\frac{18}{4}
=4+1/2
$