31/3x+20=2x

Solution for 31/3x+20=2x equation:

31/3x+20=2x

We move all terms to the left:

31/3x+20-(2x)=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+31/3x+20=0

We multiply all the terms by the denominator


-2x*3x+20*3x+31=0

Wy multiply elements

-6x^2+60x+31=0

a = -6; b = 60; c = +31;
Δ = b2-4ac
Δ = 602-4·(-6)·31
Δ = 4344
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:

$\sqrt{\Delta}=\sqrt{4344}=\sqrt{4*1086}=\sqrt{4}*\sqrt{1086}=2\sqrt{1086}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-2\sqrt{1086}}{2*-6}=\frac{-60-2\sqrt{1086}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+2\sqrt{1086}}{2*-6}=\frac{-60+2\sqrt{1086}}{-12}
$