(9x-5)*4x-7(9x-5)=0

Solution for (9x-5)*4x-7(9x-5)=0 equation:

(9x-5)*4x-7(9x-5)=0

We multiply parentheses

36x^2-20x-63x+35=0

We add all the numbers together, and all the variables

36x^2-83x+35=0

a = 36; b = -83; c = +35;
Δ = b2-4ac
Δ = -832-4·36·35
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-83)-43}{2*36}=\frac{40}{72}
=5/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-83)+43}{2*36}=\frac{126}{72}
=1+3/4
$