(2x+6)(2x-7)=0

Solution for (2x+6)(2x-7)=0 equation:

(2x+6)(2x-7)=0

We multiply parentheses ..

(+4x^2-14x+12x-42)=0

We get rid of parentheses

4x^2-14x+12x-42=0

We add all the numbers together, and all the variables

4x^2-2x-42=0

a = 4; b = -2; c = -42;
Δ = b2-4ac
Δ = -22-4·4·(-42)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-26}{2*4}=\frac{-24}{8}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+26}{2*4}=\frac{28}{8}
=3+1/2
$