(3w-7)(9+w)=0

Solution for (3w-7)(9+w)=0 equation:

(3w-7)(9+w)=0

We add all the numbers together, and all the variables

(3w-7)(w+9)=0

We multiply parentheses ..

(+3w^2+27w-7w-63)=0

We get rid of parentheses

3w^2+27w-7w-63=0

We add all the numbers together, and all the variables

3w^2+20w-63=0

a = 3; b = 20; c = -63;
Δ = b2-4ac
Δ = 202-4·3·(-63)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-34}{2*3}=\frac{-54}{6}
=-9
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+34}{2*3}=\frac{14}{6}
=2+1/3
$