(4x-5)(6x+6)=0

Solution for (4x-5)(6x+6)=0 equation:

(4x-5)(6x+6)=0

We multiply parentheses ..

(+24x^2+24x-30x-30)=0

We get rid of parentheses

24x^2+24x-30x-30=0

We add all the numbers together, and all the variables

24x^2-6x-30=0

a = 24; b = -6; c = -30;
Δ = b2-4ac
Δ = -62-4·24·(-30)
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-54}{2*24}=\frac{-48}{48}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+54}{2*24}=\frac{60}{48}
=1+1/4
$