3x-5(x-9)x=9

Solution for 3x-5(x-9)x=9 equation:

3x-5(x-9)x=9

We move all terms to the left:

3x-5(x-9)x-(9)=0

We multiply parentheses

-5x^2+3x+45x-9=0

We add all the numbers together, and all the variables

-5x^2+48x-9=0

a = -5; b = 48; c = -9;
Δ = b2-4ac
Δ = 482-4·(-5)·(-9)
Δ = 2124
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:

$\sqrt{\Delta}=\sqrt{2124}=\sqrt{36*59}=\sqrt{36}*\sqrt{59}=6\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-6\sqrt{59}}{2*-5}=\frac{-48-6\sqrt{59}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+6\sqrt{59}}{2*-5}=\frac{-48+6\sqrt{59}}{-10}
$