1/3x+2x+25=3

Solution for 1/3x+2x+25=3 equation:

1/3x+2x+25=3

We move all terms to the left:

1/3x+2x+25-(3)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2x+1/3x+22=0

We multiply all the terms by the denominator


2x*3x+22*3x+1=0

Wy multiply elements

6x^2+66x+1=0

a = 6; b = 66; c = +1;
Δ = b2-4ac
Δ = 662-4·6·1
Δ = 4332
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:

$\sqrt{\Delta}=\sqrt{4332}=\sqrt{1444*3}=\sqrt{1444}*\sqrt{3}=38\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-38\sqrt{3}}{2*6}=\frac{-66-38\sqrt{3}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+38\sqrt{3}}{2*6}=\frac{-66+38\sqrt{3}}{12}
$