5/6x=10-x

Solution for 5/6x=10-x equation:

5/6x=10-x

We move all terms to the left:

5/6x-(10-x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

5/6x-(-1x+10)=0

We get rid of parentheses

5/6x+1x-10=0

We multiply all the terms by the denominator


1x*6x-10*6x+5=0

Wy multiply elements

6x^2-60x+5=0

a = 6; b = -60; c = +5;
Δ = b2-4ac
Δ = -602-4·6·5
Δ = 3480
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:

$\sqrt{\Delta}=\sqrt{3480}=\sqrt{4*870}=\sqrt{4}*\sqrt{870}=2\sqrt{870}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{870}}{2*6}=\frac{60-2\sqrt{870}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{870}}{2*6}=\frac{60+2\sqrt{870}}{12}
$