(4w-3)*(7-w)=0

Solution for (4w-3)*(7-w)=0 equation:

(4w-3)(7-w)=0

We add all the numbers together, and all the variables

(4w-3)(-1w+7)=0

We multiply parentheses ..

(-4w^2+28w+3w-21)=0

We get rid of parentheses

-4w^2+28w+3w-21=0

We add all the numbers together, and all the variables

-4w^2+31w-21=0

a = -4; b = 31; c = -21;
Δ = b2-4ac
Δ = 312-4·(-4)·(-21)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-25}{2*-4}=\frac{-56}{-8}
=+7
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+25}{2*-4}=\frac{-6}{-8}
=3/4
$