5/6x+3x=23

Solution for 5/6x+3x=23 equation:

5/6x+3x=23

We move all terms to the left:

5/6x+3x-(23)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

3x+5/6x-23=0

We multiply all the terms by the denominator


3x*6x-23*6x+5=0

Wy multiply elements

18x^2-138x+5=0

a = 18; b = -138; c = +5;
Δ = b2-4ac
Δ = -1382-4·18·5
Δ = 18684
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:

$\sqrt{\Delta}=\sqrt{18684}=\sqrt{36*519}=\sqrt{36}*\sqrt{519}=6\sqrt{519}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-138)-6\sqrt{519}}{2*18}=\frac{138-6\sqrt{519}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-138)+6\sqrt{519}}{2*18}=\frac{138+6\sqrt{519}}{36}
$