(9x-3)(-4x+6)=12x-25

Solution for (9x-3)(-4x+6)=12x-25 equation:

(9x-3)(-4x+6)=12x-25

We move all terms to the left:

(9x-3)(-4x+6)-(12x-25)=0

We get rid of parentheses

(9x-3)(-4x+6)-12x+25=0

We multiply parentheses ..

(-36x^2+54x+12x-18)-12x+25=0

We get rid of parentheses

-36x^2+54x+12x-12x-18+25=0

We add all the numbers together, and all the variables

-36x^2+54x+7=0

a = -36; b = 54; c = +7;
Δ = b2-4ac
Δ = 542-4·(-36)·7
Δ = 3924
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3924}=\sqrt{36*109}=\sqrt{36}*\sqrt{109}=6\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-6\sqrt{109}}{2*-36}=\frac{-54-6\sqrt{109}}{-72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+6\sqrt{109}}{2*-36}=\frac{-54+6\sqrt{109}}{-72}
$