2w^2+5w=63^2

Solution for 2w^2+5w=63^2 equation:

2w^2+5w=63^2

We move all terms to the left:

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

We add all the numbers together, and all the variables

2w^2+5w-3969=0

a = 2; b = 5; c = -3969;
Δ = b2-4ac
Δ = 52-4·2·(-3969)
Δ = 31777
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{31777}}{2*2}=\frac{-5-\sqrt{31777}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{31777}}{2*2}=\frac{-5+\sqrt{31777}}{4}
$