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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

5x-3x(x-3)-(6x-11)=0

We multiply parentheses

-3x^2+5x+9x-(6x-11)=0

We get rid of parentheses

-3x^2+5x+9x-6x+11=0

We add all the numbers together, and all the variables

-3x^2+8x+11=0

a = -3; b = 8; c = +11;
Δ = b2-4ac
Δ = 82-4·(-3)·11
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-14}{2*-3}=\frac{-22}{-6}
=3+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+14}{2*-3}=\frac{6}{-6}
=-1
$