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

Solution for (5w-1)(7-w)=0 equation:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-5w^2+35w+w-7)=0

We get rid of parentheses

-5w^2+35w+w-7=0

We add all the numbers together, and all the variables

-5w^2+36w-7=0

a = -5; b = 36; c = -7;
Δ = b2-4ac
Δ = 362-4·(-5)·(-7)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-34}{2*-5}=\frac{-70}{-10}
=+7
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+34}{2*-5}=\frac{-2}{-10}
=1/5
$