(2w-3)w=152

Solution for (2w-3)w=152 equation:

(2w-3)w=152

We move all terms to the left:

(2w-3)w-(152)=0

We multiply parentheses

2w^2-3w-152=0

a = 2; b = -3; c = -152;
Δ = b2-4ac
Δ = -32-4·2·(-152)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-35}{2*2}=\frac{-32}{4}
=-8
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+35}{2*2}=\frac{38}{4}
=9+1/2
$