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

Solution for (5-w)(3w-7)=0 equation:

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

We add all the numbers together, and all the variables

(-1w+5)(3w-7)=0

We multiply parentheses ..

(-3w^2+7w+15w-35)=0

We get rid of parentheses

-3w^2+7w+15w-35=0

We add all the numbers together, and all the variables

-3w^2+22w-35=0

a = -3; b = 22; c = -35;
Δ = b2-4ac
Δ = 222-4·(-3)·(-35)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-8}{2*-3}=\frac{-30}{-6}
=+5
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+8}{2*-3}=\frac{-14}{-6}
=2+1/3
$