20-3x(2x-3)=-X

Solution for 20-3x(2x-3)=-X equation:

20-3x(2x-3)=-x

We move all terms to the left:

20-3x(2x-3)-(-x)=0

We add all the numbers together, and all the variables

-3x(2x-3)-(-1x)+20=0

We multiply parentheses

-6x^2+9x-(-1x)+20=0

We get rid of parentheses

-6x^2+9x+1x+20=0

We add all the numbers together, and all the variables

-6x^2+10x+20=0

a = -6; b = 10; c = +20;
Δ = b2-4ac
Δ = 102-4·(-6)·20
Δ = 580
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:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{145}}{2*-6}=\frac{-10-2\sqrt{145}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{145}}{2*-6}=\frac{-10+2\sqrt{145}}{-12}
$