65=(w-3)(w)

Solution for 65=(w-3)(w) equation:

65=(w-3)(w)

We move all terms to the left:

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


We calculate terms in parentheses: -((w-3)w), so:

(w-3)w

We multiply parentheses

w^2-3w

Back to the equation:

-(w^2-3w)


We get rid of parentheses

-w^2+3w+65=0

We add all the numbers together, and all the variables

-1w^2+3w+65=0

a = -1; b = 3; c = +65;
Δ = b2-4ac
Δ = 32-4·(-1)·65
Δ = 269
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{269}}{2*-1}=\frac{-3-\sqrt{269}}{-2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{269}}{2*-1}=\frac{-3+\sqrt{269}}{-2}
$