25+5/6x=x

Solution for 25+5/6x=x equation:

25+5/6x=x

We move all terms to the left:

25+5/6x-(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

-1x+5/6x+25=0

We multiply all the terms by the denominator


-1x*6x+25*6x+5=0

Wy multiply elements

-6x^2+150x+5=0

a = -6; b = 150; c = +5;
Δ = b2-4ac
Δ = 1502-4·(-6)·5
Δ = 22620
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:

$\sqrt{\Delta}=\sqrt{22620}=\sqrt{4*5655}=\sqrt{4}*\sqrt{5655}=2\sqrt{5655}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-2\sqrt{5655}}{2*-6}=\frac{-150-2\sqrt{5655}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+2\sqrt{5655}}{2*-6}=\frac{-150+2\sqrt{5655}}{-12}
$