0.5x+6/3x=x+26

Solution for 0.5x+6/3x=x+26 equation:

0.5x+6/3x=x+26

We move all terms to the left:

0.5x+6/3x-(x+26)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

0.5x+6/3x-x-26=0

We multiply all the terms by the denominator


(0.5x)*3x-x*3x-26*3x+6=0

We add all the numbers together, and all the variables

(+0.5x)*3x-x*3x-26*3x+6=0

We multiply parentheses

0x^2-x*3x-26*3x+6=0

Wy multiply elements

0x^2-3x^2-78x+6=0

We add all the numbers together, and all the variables

-2x^2-78x+6=0

a = -2; b = -78; c = +6;
Δ = b2-4ac
Δ = -782-4·(-2)·6
Δ = 6132
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:

$\sqrt{\Delta}=\sqrt{6132}=\sqrt{4*1533}=\sqrt{4}*\sqrt{1533}=2\sqrt{1533}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-2\sqrt{1533}}{2*-2}=\frac{78-2\sqrt{1533}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+2\sqrt{1533}}{2*-2}=\frac{78+2\sqrt{1533}}{-4}
$