2+x(x-6)=x-3(4-x)

Solution for 2+x(x-6)=x-3(4-x) equation:

2+x(x-6)=x-3(4-x)

We move all terms to the left:

2+x(x-6)-(x-3(4-x))=0

We add all the numbers together, and all the variables

x(x-6)-(x-3(-1x+4))+2=0

We multiply parentheses

x^2-6x-(x-3(-1x+4))+2=0


We calculate terms in parentheses: -(x-3(-1x+4)), so:

x-3(-1x+4)

We multiply parentheses

x+3x-12

We add all the numbers together, and all the variables

4x-12

Back to the equation:

-(4x-12)


We get rid of parentheses

x^2-6x-4x+12+2=0

We add all the numbers together, and all the variables

x^2-10x+14=0

a = 1; b = -10; c = +14;
Δ = b2-4ac
Δ = -102-4·1·14
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{11}}{2*1}=\frac{10-2\sqrt{11}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{11}}{2*1}=\frac{10+2\sqrt{11}}{2}
$