2+3x(x-4)-2(x-5)=x

Solution for 2+3x(x-4)-2(x-5)=x equation:

2+3x(x-4)-2(x-5)=x

We move all terms to the left:

2+3x(x-4)-2(x-5)-(x)=0

We add all the numbers together, and all the variables

-1x+3x(x-4)-2(x-5)+2=0

We multiply parentheses

3x^2-1x-12x-2x+10+2=0

We add all the numbers together, and all the variables

3x^2-15x+12=0

a = 3; b = -15; c = +12;
Δ = b2-4ac
Δ = -152-4·3·12
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-9}{2*3}=\frac{6}{6}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+9}{2*3}=\frac{24}{6}
=4
$