(7x-6)(6x+8)=0

Solution for (7x-6)(6x+8)=0 equation:

(7x-6)(6x+8)=0

We multiply parentheses ..

(+42x^2+56x-36x-48)=0

We get rid of parentheses

42x^2+56x-36x-48=0

We add all the numbers together, and all the variables

42x^2+20x-48=0

a = 42; b = 20; c = -48;
Δ = b2-4ac
Δ = 202-4·42·(-48)
Δ = 8464
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8464}=92$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-92}{2*42}=\frac{-112}{84}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+92}{2*42}=\frac{72}{84}
=6/7
$