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

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

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

We multiply parentheses ..

(+42x^2+49x-36x-42)=0

We get rid of parentheses

42x^2+49x-36x-42=0

We add all the numbers together, and all the variables

42x^2+13x-42=0

a = 42; b = 13; c = -42;
Δ = b2-4ac
Δ = 132-4·42·(-42)
Δ = 7225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7225}=85$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-85}{2*42}=\frac{-98}{84}
=-1+1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+85}{2*42}=\frac{72}{84}
=6/7
$