2w^2-3w=65^2

Solution for 2w^2-3w=65^2 equation:

2w^2-3w=65^2

We move all terms to the left:

2w^2-3w-(65^2)=0

We add all the numbers together, and all the variables

2w^2-3w-4225=0

a = 2; b = -3; c = -4225;
Δ = b2-4ac
Δ = -32-4·2·(-4225)
Δ = 33809
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{-(-3)-\sqrt{33809}}{2*2}=\frac{3-\sqrt{33809}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{33809}}{2*2}=\frac{3+\sqrt{33809}}{4}
$