12+11/6x=5+3x

Solution for 12+11/6x=5+3x equation:

12+11/6x=5+3x

We move all terms to the left:

12+11/6x-(5+3x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

11/6x-(3x+5)+12=0

We get rid of parentheses

11/6x-3x-5+12=0

We multiply all the terms by the denominator


-3x*6x-5*6x+12*6x+11=0

Wy multiply elements

-18x^2-30x+72x+11=0

We add all the numbers together, and all the variables

-18x^2+42x+11=0

a = -18; b = 42; c = +11;
Δ = b2-4ac
Δ = 422-4·(-18)·11
Δ = 2556
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:

$\sqrt{\Delta}=\sqrt{2556}=\sqrt{36*71}=\sqrt{36}*\sqrt{71}=6\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-6\sqrt{71}}{2*-18}=\frac{-42-6\sqrt{71}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+6\sqrt{71}}{2*-18}=\frac{-42+6\sqrt{71}}{-36}
$