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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

4w^2-3w+28w-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
$