5/6x+90=x

Solution for 5/6x+90=x equation:

5/6x+90=x

We move all terms to the left:

5/6x+90-(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+90=0

We multiply all the terms by the denominator


-1x*6x+90*6x+5=0

Wy multiply elements

-6x^2+540x+5=0

a = -6; b = 540; c = +5;
Δ = b2-4ac
Δ = 5402-4·(-6)·5
Δ = 291720
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:

$\sqrt{\Delta}=\sqrt{291720}=\sqrt{4*72930}=\sqrt{4}*\sqrt{72930}=2\sqrt{72930}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(540)-2\sqrt{72930}}{2*-6}=\frac{-540-2\sqrt{72930}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(540)+2\sqrt{72930}}{2*-6}=\frac{-540+2\sqrt{72930}}{-12}
$