X+8/3x=44

Solution for X+8/3x=44 equation:

X+8/3X=44

We move all terms to the left:

X+8/3X-(44)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We multiply all the terms by the denominator


X*3X-44*3X+8=0

Wy multiply elements

3X^2-132X+8=0

a = 3; b = -132; c = +8;
Δ = b2-4ac
Δ = -1322-4·3·8
Δ = 17328
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:

$\sqrt{\Delta}=\sqrt{17328}=\sqrt{5776*3}=\sqrt{5776}*\sqrt{3}=76\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-132)-76\sqrt{3}}{2*3}=\frac{132-76\sqrt{3}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-132)+76\sqrt{3}}{2*3}=\frac{132+76\sqrt{3}}{6}
$