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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-5w^2+35w+2w-14)=0

We get rid of parentheses

-5w^2+35w+2w-14=0

We add all the numbers together, and all the variables

-5w^2+37w-14=0

a = -5; b = 37; c = -14;
Δ = b2-4ac
Δ = 372-4·(-5)·(-14)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-33}{2*-5}=\frac{-70}{-10}
=+7
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+33}{2*-5}=\frac{-4}{-10}
=2/5
$