X(6x+10)=(x+2)

Solution for X(6x+10)=(x+2) equation:

X(6X+10)=(X+2)

We move all terms to the left:

X(6X+10)-((X+2))=0

We multiply parentheses

6X^2+10X-((X+2))=0


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

(X+2)

We get rid of parentheses

X+2

Back to the equation:

-(X+2)


We get rid of parentheses

6X^2+10X-X-2=0

We add all the numbers together, and all the variables

6X^2+9X-2=0

a = 6; b = 9; c = -2;
Δ = b2-4ac
Δ = 92-4·6·(-2)
Δ = 129
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{-(9)-\sqrt{129}}{2*6}=\frac{-9-\sqrt{129}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{129}}{2*6}=\frac{-9+\sqrt{129}}{12}
$