(4w+7)(2-w)=0

Solution for (4w+7)(2-w)=0 equation:

(4w+7)(2-w)=0

We add all the numbers together, and all the variables

(4w+7)(-1w+2)=0

We multiply parentheses ..

(-4w^2+8w-7w+14)=0

We get rid of parentheses

-4w^2+8w-7w+14=0

We add all the numbers together, and all the variables

-4w^2+w+14=0

a = -4; b = 1; c = +14;
Δ = b2-4ac
Δ = 12-4·(-4)·14
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-15}{2*-4}=\frac{-16}{-8}
=+2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+15}{2*-4}=\frac{14}{-8}
=-1+3/4
$