(-2x+4)(x+7)=28

Solution for (-2x+4)(x+7)=28 equation:

(-2x+4)(x+7)=28

We move all terms to the left:

(-2x+4)(x+7)-(28)=0

We multiply parentheses ..

(-2x^2-14x+4x+28)-28=0

We get rid of parentheses

-2x^2-14x+4x+28-28=0

We add all the numbers together, and all the variables

-2x^2-10x=0

a = -2; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·(-2)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*-2}=\frac{0}{-4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*-2}=\frac{20}{-4}
=-5
$