20/3x-2x=10

Solution for 20/3x-2x=10 equation:

20/3x-2x=10

We move all terms to the left:

20/3x-2x-(10)=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+20/3x-10=0

We multiply all the terms by the denominator


-2x*3x-10*3x+20=0

Wy multiply elements

-6x^2-30x+20=0

a = -6; b = -30; c = +20;
Δ = b2-4ac
Δ = -302-4·(-6)·20
Δ = 1380
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:

$\sqrt{\Delta}=\sqrt{1380}=\sqrt{4*345}=\sqrt{4}*\sqrt{345}=2\sqrt{345}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{345}}{2*-6}=\frac{30-2\sqrt{345}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{345}}{2*-6}=\frac{30+2\sqrt{345}}{-12}
$