(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+25w+21=0

a = -4; b = 25; c = +21;
Δ = b2-4ac
Δ = 252-4·(-4)·21
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-31}{2*-4}=\frac{-56}{-8}
=+7
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+31}{2*-4}=\frac{6}{-8}
=-3/4
$