65=(3w-2)(w)

Solution for 65=(3w-2)(w) equation:

65=(3w-2)(w)

We move all terms to the left:

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


We calculate terms in parentheses: -((3w-2)w), so:

(3w-2)w

We multiply parentheses

3w^2-2w

Back to the equation:

-(3w^2-2w)


We get rid of parentheses

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

a = -3; b = 2; c = +65;
Δ = b2-4ac
Δ = 22-4·(-3)·65
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-28}{2*-3}=\frac{-30}{-6}
=+5
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+28}{2*-3}=\frac{26}{-6}
=-4+1/3
$