(3w-4)(5-w)=0

Solution for (3w-4)(5-w)=0 equation:

(3w-4)(5-w)=0

We add all the numbers together, and all the variables

(3w-4)(-1w+5)=0

We multiply parentheses ..

(-3w^2+15w+4w-20)=0

We get rid of parentheses

-3w^2+15w+4w-20=0

We add all the numbers together, and all the variables

-3w^2+19w-20=0

a = -3; b = 19; c = -20;
Δ = b2-4ac
Δ = 192-4·(-3)·(-20)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-11}{2*-3}=\frac{-30}{-6}
=+5
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+11}{2*-3}=\frac{-8}{-6}
=1+1/3
$