3x+2/x-5=20

Solution for 3x+2/x-5=20 equation:

3x+2/x-5=20

We move all terms to the left:

3x+2/x-5-(20)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

3x+2/x-25=0

We multiply all the terms by the denominator


3x*x-25*x+2=0

We add all the numbers together, and all the variables

-25x+3x*x+2=0

Wy multiply elements

3x^2-25x+2=0

a = 3; b = -25; c = +2;
Δ = b2-4ac
Δ = -252-4·3·2
Δ = 601
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{-(-25)-\sqrt{601}}{2*3}=\frac{25-\sqrt{601}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{601}}{2*3}=\frac{25+\sqrt{601}}{6}
$