X/6X+20=12+2x

Solution for X/6X+20=12+2x equation:

X/6X+20=12+2X

We move all terms to the left:

X/6X+20-(12+2X)=0


Domain of the equation: 6X!=0

X!=0/6

X!=0

X∈R


We add all the numbers together, and all the variables

X/6X-(2X+12)+20=0

We get rid of parentheses

X/6X-2X-12+20=0

We multiply all the terms by the denominator


X-2X*6X-12*6X+20*6X=0

Wy multiply elements

-12X^2+X-72X+120X=0

We add all the numbers together, and all the variables

-12X^2+49X=0

a = -12; b = 49; c = 0;
Δ = b2-4ac
Δ = 492-4·(-12)·0
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(49)-49}{2*-12}=\frac{-98}{-24}
=4+1/12
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+49}{2*-12}=\frac{0}{-24}
=0
$