77=w(2w-3)

Solution for 77=w(2w-3) equation:

77=w(2w-3)

We move all terms to the left:

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


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

w(2w-3)

We multiply parentheses

2w^2-3w

Back to the equation:

-(2w^2-3w)


We get rid of parentheses

-2w^2+3w+77=0

a = -2; b = 3; c = +77;
Δ = b2-4ac
Δ = 32-4·(-2)·77
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-25}{2*-2}=\frac{-28}{-4}
=+7
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+25}{2*-2}=\frac{22}{-4}
=-5+1/2
$