0.5+8/3x=x+26

Solution for 0.5+8/3x=x+26 equation:

0.5+8/3x=x+26

We move all terms to the left:

0.5+8/3x-(x+26)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

8/3x-x-26+0.5=0

We multiply all the terms by the denominator


-x*3x-26*3x+(0.5)*3x+8=0

We multiply parentheses

-x*3x-26*3x+1.5x+8=0

Wy multiply elements

-3x^2-78x+1.5x+8=0

We add all the numbers together, and all the variables

-3x^2-76.5x+8=0

a = -3; b = -76.5; c = +8;
Δ = b2-4ac
Δ = -76.52-4·(-3)·8
Δ = 5948.25
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{-(-76.5)-\sqrt{5948.25}}{2*-3}=\frac{76.5-\sqrt{5948.25}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76.5)+\sqrt{5948.25}}{2*-3}=\frac{76.5+\sqrt{5948.25}}{-6}
$