(3w-7)(8+w)=0

Solution for (3w-7)(8+w)=0 equation:

(3w-7)(8+w)=0

We add all the numbers together, and all the variables

(3w-7)(w+8)=0

We multiply parentheses ..

(+3w^2+24w-7w-56)=0

We get rid of parentheses

3w^2+24w-7w-56=0

We add all the numbers together, and all the variables

3w^2+17w-56=0

a = 3; b = 17; c = -56;
Δ = b2-4ac
Δ = 172-4·3·(-56)
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{-(17)-31}{2*3}=\frac{-48}{6}
=-8
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+31}{2*3}=\frac{14}{6}
=2+1/3
$