0.6+2x+10.4+x+5/12x=52

Solution for 0.6+2x+10.4+x+5/12x=52 equation:

0.6+2x+10.4+x+5/12x=52

We move all terms to the left:

0.6+2x+10.4+x+5/12x-(52)=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R


We add all the numbers together, and all the variables

3x+5/12x-41=0

We multiply all the terms by the denominator


3x*12x-41*12x+5=0

Wy multiply elements

36x^2-492x+5=0

a = 36; b = -492; c = +5;
Δ = b2-4ac
Δ = -4922-4·36·5
Δ = 241344
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:

$\sqrt{\Delta}=\sqrt{241344}=\sqrt{576*419}=\sqrt{576}*\sqrt{419}=24\sqrt{419}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-492)-24\sqrt{419}}{2*36}=\frac{492-24\sqrt{419}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-492)+24\sqrt{419}}{2*36}=\frac{492+24\sqrt{419}}{72}
$