(5w-7)(2-w)=0

Solution for (5w-7)(2-w)=0 equation:

(5w-7)(2-w)=0

We add all the numbers together, and all the variables

(5w-7)(-1w+2)=0

We multiply parentheses ..

(-5w^2+10w+7w-14)=0

We get rid of parentheses

-5w^2+10w+7w-14=0

We add all the numbers together, and all the variables

-5w^2+17w-14=0

a = -5; b = 17; c = -14;
Δ = b2-4ac
Δ = 172-4·(-5)·(-14)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-3}{2*-5}=\frac{-20}{-10}
=+2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+3}{2*-5}=\frac{-14}{-10}
=1+2/5
$