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

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

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

We multiply parentheses ..

(+3w^2-8w-21w+56)=0

We get rid of parentheses

3w^2-8w-21w+56=0

We add all the numbers together, and all the variables

3w^2-29w+56=0

a = 3; b = -29; c = +56;
Δ = b2-4ac
Δ = -292-4·3·56
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-13}{2*3}=\frac{16}{6}
=2+2/3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+13}{2*3}=\frac{42}{6}
=7
$