2/6x+15=x-6

Solution for 2/6x+15=x-6 equation:

2/6x+15=x-6

We move all terms to the left:

2/6x+15-(x-6)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

2/6x-x+6+15=0

We multiply all the terms by the denominator


-x*6x+6*6x+15*6x+2=0

Wy multiply elements

-6x^2+36x+90x+2=0

We add all the numbers together, and all the variables

-6x^2+126x+2=0

a = -6; b = 126; c = +2;
Δ = b2-4ac
Δ = 1262-4·(-6)·2
Δ = 15924
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:

$\sqrt{\Delta}=\sqrt{15924}=\sqrt{4*3981}=\sqrt{4}*\sqrt{3981}=2\sqrt{3981}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(126)-2\sqrt{3981}}{2*-6}=\frac{-126-2\sqrt{3981}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(126)+2\sqrt{3981}}{2*-6}=\frac{-126+2\sqrt{3981}}{-12}
$