x=5/6x+100

Solution for x=5/6x+100 equation:

x=5/6x+100

We move all terms to the left:

x-(5/6x+100)=0


Domain of the equation: 6x+100)!=0

x∈R


We get rid of parentheses

x-5/6x-100=0

We multiply all the terms by the denominator


x*6x-100*6x-5=0

Wy multiply elements

6x^2-600x-5=0

a = 6; b = -600; c = -5;
Δ = b2-4ac
Δ = -6002-4·6·(-5)
Δ = 360120
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:

$\sqrt{\Delta}=\sqrt{360120}=\sqrt{4*90030}=\sqrt{4}*\sqrt{90030}=2\sqrt{90030}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-600)-2\sqrt{90030}}{2*6}=\frac{600-2\sqrt{90030}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-600)+2\sqrt{90030}}{2*6}=\frac{600+2\sqrt{90030}}{12}
$