76=(3w+7)w

Solution for 76=(3w+7)w equation:

76=(3w+7)w

We move all terms to the left:

76-((3w+7)w)=0


We calculate terms in parentheses: -((3w+7)w), so:

(3w+7)w

We multiply parentheses

3w^2+7w

Back to the equation:

-(3w^2+7w)


We get rid of parentheses

-3w^2-7w+76=0

a = -3; b = -7; c = +76;
Δ = b2-4ac
Δ = -72-4·(-3)·76
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-31}{2*-3}=\frac{-24}{-6}
=+4
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+31}{2*-3}=\frac{38}{-6}
=-6+1/3
$