6x+3(3-2x)5x-11=x

Solution for 6x+3(3-2x)5x-11=x equation:

6x+3(3-2x)5x-11=x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

5x+3(-2x+3)5x-11=0

We multiply parentheses

-30x^2+5x+45x-11=0

We add all the numbers together, and all the variables

-30x^2+50x-11=0

a = -30; b = 50; c = -11;
Δ = b2-4ac
Δ = 502-4·(-30)·(-11)
Δ = 1180
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:

$\sqrt{\Delta}=\sqrt{1180}=\sqrt{4*295}=\sqrt{4}*\sqrt{295}=2\sqrt{295}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{295}}{2*-30}=\frac{-50-2\sqrt{295}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{295}}{2*-30}=\frac{-50+2\sqrt{295}}{-60}
$