(5w-6)(7-w)=0

Solution for (5w-6)(7-w)=0 equation:

(5w-6)(7-w)=0

We add all the numbers together, and all the variables

(5w-6)(-1w+7)=0

We multiply parentheses ..

(-5w^2+35w+6w-42)=0

We get rid of parentheses

-5w^2+35w+6w-42=0

We add all the numbers together, and all the variables

-5w^2+41w-42=0

a = -5; b = 41; c = -42;
Δ = b2-4ac
Δ = 412-4·(-5)·(-42)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-29}{2*-5}=\frac{-70}{-10}
=+7
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+29}{2*-5}=\frac{-12}{-10}
=1+1/5
$