(3w-7)(6+w)=0

Solution for (3w-7)(6+w)=0 equation:

(3w-7)(6+w)=0

We add all the numbers together, and all the variables

(3w-7)(w+6)=0

We multiply parentheses ..

(+3w^2+18w-7w-42)=0

We get rid of parentheses

3w^2+18w-7w-42=0

We add all the numbers together, and all the variables

3w^2+11w-42=0

a = 3; b = 11; c = -42;
Δ = b2-4ac
Δ = 112-4·3·(-42)
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{-(11)-25}{2*3}=\frac{-36}{6}
=-6
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+25}{2*3}=\frac{14}{6}
=2+1/3
$