6x+2/3x=x+20

Solution for 6x+2/3x=x+20 equation:

6x+2/3x=x+20

We move all terms to the left:

6x+2/3x-(x+20)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

6x+2/3x-x-20=0

We multiply all the terms by the denominator


6x*3x-x*3x-20*3x+2=0

Wy multiply elements

18x^2-3x^2-60x+2=0

We add all the numbers together, and all the variables

15x^2-60x+2=0

a = 15; b = -60; c = +2;
Δ = b2-4ac
Δ = -602-4·15·2
Δ = 3480
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:

$\sqrt{\Delta}=\sqrt{3480}=\sqrt{4*870}=\sqrt{4}*\sqrt{870}=2\sqrt{870}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{870}}{2*15}=\frac{60-2\sqrt{870}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{870}}{2*15}=\frac{60+2\sqrt{870}}{30}
$