0.5x+8/3x=x+39

Solution for 0.5x+8/3x=x+39 equation:

0.5x+8/3x=x+39

We move all terms to the left:

0.5x+8/3x-(x+39)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

0.5x+8/3x-x-39=0

We multiply all the terms by the denominator


(0.5x)*3x-x*3x-39*3x+8=0

We add all the numbers together, and all the variables

(+0.5x)*3x-x*3x-39*3x+8=0

We multiply parentheses

0x^2-x*3x-39*3x+8=0

Wy multiply elements

0x^2-3x^2-117x+8=0

We add all the numbers together, and all the variables

-2x^2-117x+8=0

a = -2; b = -117; c = +8;
Δ = b2-4ac
Δ = -1172-4·(-2)·8
Δ = 13753
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-117)-\sqrt{13753}}{2*-2}=\frac{117-\sqrt{13753}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-117)+\sqrt{13753}}{2*-2}=\frac{117+\sqrt{13753}}{-4}
$