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

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

X(X-3)=(X+4)+2

We move all terms to the left:

X(X-3)-((X+4)+2)=0

We multiply parentheses

X^2-3X-((X+4)+2)=0


We calculate terms in parentheses: -((X+4)+2), so:

(X+4)+2

We get rid of parentheses

X+4+2

We add all the numbers together, and all the variables

X+6

Back to the equation:

-(X+6)


We get rid of parentheses

X^2-3X-X-6=0

We add all the numbers together, and all the variables

X^2-4X-6=0

a = 1; b = -4; c = -6;
Δ = b2-4ac
Δ = -42-4·1·(-6)
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{10}}{2*1}=\frac{4-2\sqrt{10}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{10}}{2*1}=\frac{4+2\sqrt{10}}{2}
$