124=5/6x+x

Solution for 124=5/6x+x equation:

124=5/6x+x

We move all terms to the left:

124-(5/6x+x)=0


Domain of the equation: 6x+x)!=0

x∈R


We add all the numbers together, and all the variables

-(+x+5/6x)+124=0

We get rid of parentheses

-x-5/6x+124=0

We multiply all the terms by the denominator


-x*6x+124*6x-5=0

Wy multiply elements

-6x^2+744x-5=0

a = -6; b = 744; c = -5;
Δ = b2-4ac
Δ = 7442-4·(-6)·(-5)
Δ = 553416
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:

$\sqrt{\Delta}=\sqrt{553416}=\sqrt{4*138354}=\sqrt{4}*\sqrt{138354}=2\sqrt{138354}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(744)-2\sqrt{138354}}{2*-6}=\frac{-744-2\sqrt{138354}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(744)+2\sqrt{138354}}{2*-6}=\frac{-744+2\sqrt{138354}}{-12}
$