2+x=5+10/12x

Solution for 2+x=5+10/12x equation:

2+x=5+10/12x

We move all terms to the left:

2+x-(5+10/12x)=0


Domain of the equation: 12x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(10/12x+5)+2=0

We get rid of parentheses

x-10/12x-5+2=0

We multiply all the terms by the denominator


x*12x-5*12x+2*12x-10=0

Wy multiply elements

12x^2-60x+24x-10=0

We add all the numbers together, and all the variables

12x^2-36x-10=0

a = 12; b = -36; c = -10;
Δ = b2-4ac
Δ = -362-4·12·(-10)
Δ = 1776
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:

$\sqrt{\Delta}=\sqrt{1776}=\sqrt{16*111}=\sqrt{16}*\sqrt{111}=4\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{111}}{2*12}=\frac{36-4\sqrt{111}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{111}}{2*12}=\frac{36+4\sqrt{111}}{24}
$