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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: x-3)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

2x+x*x-20=0

Wy multiply elements

x^2+2x-20=0

a = 1; b = 2; c = -20;
Δ = b2-4ac
Δ = 22-4·1·(-20)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{21}}{2*1}=\frac{-2-2\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{21}}{2*1}=\frac{-2+2\sqrt{21}}{2}
$