20+3x+2/3x=8

Solution for 20+3x+2/3x=8 equation:

20+3x+2/3x=8

We move all terms to the left:

20+3x+2/3x-(8)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

3x+2/3x+12=0

We multiply all the terms by the denominator


3x*3x+12*3x+2=0

Wy multiply elements

9x^2+36x+2=0

a = 9; b = 36; c = +2;
Δ = b2-4ac
Δ = 362-4·9·2
Δ = 1224
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:

$\sqrt{\Delta}=\sqrt{1224}=\sqrt{36*34}=\sqrt{36}*\sqrt{34}=6\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-6\sqrt{34}}{2*9}=\frac{-36-6\sqrt{34}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+6\sqrt{34}}{2*9}=\frac{-36+6\sqrt{34}}{18}
$