(7w-8)(2w-3)=0

Solution for (7w-8)(2w-3)=0 equation:

(7w-8)(2w-3)=0

We multiply parentheses ..

(+14w^2-21w-16w+24)=0

We get rid of parentheses

14w^2-21w-16w+24=0

We add all the numbers together, and all the variables

14w^2-37w+24=0

a = 14; b = -37; c = +24;
Δ = b2-4ac
Δ = -372-4·14·24
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-5}{2*14}=\frac{32}{28}
=1+1/7
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+5}{2*14}=\frac{42}{28}
=1+1/2
$