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

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

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

We multiply parentheses ..

(+36x^2+81x-28x-63)=0

We get rid of parentheses

36x^2+81x-28x-63=0

We add all the numbers together, and all the variables

36x^2+53x-63=0

a = 36; b = 53; c = -63;
Δ = b2-4ac
Δ = 532-4·36·(-63)
Δ = 11881
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11881}=109$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(53)-109}{2*36}=\frac{-162}{72}
=-2+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(53)+109}{2*36}=\frac{56}{72}
=7/9
$