x+6/x-3=20

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

x+6/x-3=20

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+6/x-23=0

We multiply all the terms by the denominator


x*x-23*x+6=0

We add all the numbers together, and all the variables

-23x+x*x+6=0

Wy multiply elements

x^2-23x+6=0

a = 1; b = -23; c = +6;
Δ = b2-4ac
Δ = -232-4·1·6
Δ = 505
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-\sqrt{505}}{2*1}=\frac{23-\sqrt{505}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{505}}{2*1}=\frac{23+\sqrt{505}}{2}
$