(2w+3)*w=77^2

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

(2w+3)*w=77^2

We move all terms to the left:

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

We add all the numbers together, and all the variables

(2w+3)*w-5929=0

We multiply parentheses

2w^2+3w-5929=0

a = 2; b = 3; c = -5929;
Δ = b2-4ac
Δ = 32-4·2·(-5929)
Δ = 47441
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{47441}}{2*2}=\frac{-3-\sqrt{47441}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{47441}}{2*2}=\frac{-3+\sqrt{47441}}{4}
$