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

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

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

We multiply parentheses ..

(+4x^2+8x-14x-28)=0

We get rid of parentheses

4x^2+8x-14x-28=0

We add all the numbers together, and all the variables

4x^2-6x-28=0

a = 4; b = -6; c = -28;
Δ = b2-4ac
Δ = -62-4·4·(-28)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-22}{2*4}=\frac{-16}{8}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+22}{2*4}=\frac{28}{8}
=3+1/2
$