X/2x+6=6x-2

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

X/2X+6=6X-2

We move all terms to the left:

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


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We get rid of parentheses

X/2X-6X+2+6=0

We multiply all the terms by the denominator


X-6X*2X+2*2X+6*2X=0

Wy multiply elements

-12X^2+X+4X+12X=0

We add all the numbers together, and all the variables

-12X^2+17X=0

a = -12; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-12)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-12}=\frac{-34}{-24}
=1+5/12
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-12}=\frac{0}{-24}
=0
$