-9x(3x-5)=6x

Solution for -9x(3x-5)=6x equation:

-9x(3x-5)=6x

We move all terms to the left:

-9x(3x-5)-(6x)=0

We add all the numbers together, and all the variables

-6x-9x(3x-5)=0

We multiply parentheses

-27x^2-6x+45x=0

We add all the numbers together, and all the variables

-27x^2+39x=0

a = -27; b = 39; c = 0;
Δ = b2-4ac
Δ = 392-4·(-27)·0
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-39}{2*-27}=\frac{-78}{-54}
=1+4/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+39}{2*-27}=\frac{0}{-54}
=0
$