w(2w-5)=117

Solution for w(2w-5)=117 equation:

w(2w-5)=117

We move all terms to the left:

w(2w-5)-(117)=0

We multiply parentheses

2w^2-5w-117=0

a = 2; b = -5; c = -117;
Δ = b2-4ac
Δ = -52-4·2·(-117)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-31}{2*2}=\frac{-26}{4}
=-6+1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+31}{2*2}=\frac{36}{4}
=9
$