X(x+6)=(x+3)

Solution for X(x+6)=(x+3) equation:

X(X+6)=(X+3)

We move all terms to the left:

X(X+6)-((X+3))=0

We multiply parentheses

X^2+6X-((X+3))=0


We calculate terms in parentheses: -((X+3)), so:

(X+3)

We get rid of parentheses

X+3

Back to the equation:

-(X+3)


We get rid of parentheses

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

We add all the numbers together, and all the variables

X^2+5X-3=0

a = 1; b = 5; c = -3;
Δ = b2-4ac
Δ = 52-4·1·(-3)
Δ = 37
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{37}}{2*1}=\frac{-5-\sqrt{37}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{37}}{2*1}=\frac{-5+\sqrt{37}}{2}
$