6x+2/2x=x+23

Solution for 6x+2/2x=x+23 equation:

6x+2/2x=x+23

We move all terms to the left:

6x+2/2x-(x+23)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

6x+2/2x-x-23=0

We multiply all the terms by the denominator


6x*2x-x*2x-23*2x+2=0

Wy multiply elements

12x^2-2x^2-46x+2=0

We add all the numbers together, and all the variables

10x^2-46x+2=0

a = 10; b = -46; c = +2;
Δ = b2-4ac
Δ = -462-4·10·2
Δ = 2036
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:

$\sqrt{\Delta}=\sqrt{2036}=\sqrt{4*509}=\sqrt{4}*\sqrt{509}=2\sqrt{509}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{509}}{2*10}=\frac{46-2\sqrt{509}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{509}}{2*10}=\frac{46+2\sqrt{509}}{20}
$