2w^2+5w=133^2

Solution for 2w^2+5w=133^2 equation:

2w^2+5w=133^2

We move all terms to the left:

2w^2+5w-(133^2)=0

We add all the numbers together, and all the variables

2w^2+5w-17689=0

a = 2; b = 5; c = -17689;
Δ = b2-4ac
Δ = 52-4·2·(-17689)
Δ = 141537
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{141537}}{2*2}=\frac{-5-\sqrt{141537}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{141537}}{2*2}=\frac{-5+\sqrt{141537}}{4}
$