(4x-6)(9x+7)=0

Solution for (4x-6)(9x+7)=0 equation:

(4x-6)(9x+7)=0

We multiply parentheses ..

(+36x^2+28x-54x-42)=0

We get rid of parentheses

36x^2+28x-54x-42=0

We add all the numbers together, and all the variables

36x^2-26x-42=0

a = 36; b = -26; c = -42;
Δ = b2-4ac
Δ = -262-4·36·(-42)
Δ = 6724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6724}=82$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-82}{2*36}=\frac{-56}{72}
=-7/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+82}{2*36}=\frac{108}{72}
=1+1/2
$