(3w+7)w=66

Solution for (3w+7)w=66 equation:

(3w+7)w=66

We move all terms to the left:

(3w+7)w-(66)=0

We multiply parentheses

3w^2+7w-66=0

a = 3; b = 7; c = -66;
Δ = b2-4ac
Δ = 72-4·3·(-66)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-29}{2*3}=\frac{-36}{6}
=-6
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+29}{2*3}=\frac{22}{6}
=3+2/3
$