3x-20/x+4=5

Solution for 3x-20/x+4=5 equation:

3x-20/x+4=5

We move all terms to the left:

3x-20/x+4-(5)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

3x-20/x-1=0

We multiply all the terms by the denominator


3x*x-1*x-20=0

We add all the numbers together, and all the variables

-1x+3x*x-20=0

Wy multiply elements

3x^2-1x-20=0

a = 3; b = -1; c = -20;
Δ = b2-4ac
Δ = -12-4·3·(-20)
Δ = 241
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{-(-1)-\sqrt{241}}{2*3}=\frac{1-\sqrt{241}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{241}}{2*3}=\frac{1+\sqrt{241}}{6}
$