x+5/6x=44

Solution for x+5/6x=44 equation:

x+5/6x=44

We move all terms to the left:

x+5/6x-(44)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We multiply all the terms by the denominator


x*6x-44*6x+5=0

Wy multiply elements

6x^2-264x+5=0

a = 6; b = -264; c = +5;
Δ = b2-4ac
Δ = -2642-4·6·5
Δ = 69576
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:

$\sqrt{\Delta}=\sqrt{69576}=\sqrt{4*17394}=\sqrt{4}*\sqrt{17394}=2\sqrt{17394}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-264)-2\sqrt{17394}}{2*6}=\frac{264-2\sqrt{17394}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-264)+2\sqrt{17394}}{2*6}=\frac{264+2\sqrt{17394}}{12}
$