(7x-6)(6x+9)=0

Solution for (7x-6)(6x+9)=0 equation:

(7x-6)(6x+9)=0

We multiply parentheses ..

(+42x^2+63x-36x-54)=0

We get rid of parentheses

42x^2+63x-36x-54=0

We add all the numbers together, and all the variables

42x^2+27x-54=0

a = 42; b = 27; c = -54;
Δ = b2-4ac
Δ = 272-4·42·(-54)
Δ = 9801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9801}=99$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-99}{2*42}=\frac{-126}{84}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+99}{2*42}=\frac{72}{84}
=6/7
$