(4x-7)(6x+6)=0

Solution for (4x-7)(6x+6)=0 equation:

(4x-7)(6x+6)=0

We multiply parentheses ..

(+24x^2+24x-42x-42)=0

We get rid of parentheses

24x^2+24x-42x-42=0

We add all the numbers together, and all the variables

24x^2-18x-42=0

a = 24; b = -18; c = -42;
Δ = b2-4ac
Δ = -182-4·24·(-42)
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-66}{2*24}=\frac{-48}{48}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+66}{2*24}=\frac{84}{48}
=1+3/4
$