77=(2w+3)(w)

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

77=(2w+3)(w)

We move all terms to the left:

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


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

(2w+3)w

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