x+(5/6x)=33

Solution for x+(5/6x)=33 equation:

x+(5/6x)=33

We move all terms to the left:

x+(5/6x)-(33)=0


Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x+(+5/6x)-33=0

We get rid of parentheses

x+5/6x-33=0

We multiply all the terms by the denominator


x*6x-33*6x+5=0

Wy multiply elements

6x^2-198x+5=0

a = 6; b = -198; c = +5;
Δ = b2-4ac
Δ = -1982-4·6·5
Δ = 39084
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:

$\sqrt{\Delta}=\sqrt{39084}=\sqrt{4*9771}=\sqrt{4}*\sqrt{9771}=2\sqrt{9771}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-198)-2\sqrt{9771}}{2*6}=\frac{198-2\sqrt{9771}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-198)+2\sqrt{9771}}{2*6}=\frac{198+2\sqrt{9771}}{12}
$