4x-20/x=6

Solution for 4x-20/x=6 equation:

4x-20/x=6

We move all terms to the left:

4x-20/x-(6)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


4x*x-6*x-20=0

We add all the numbers together, and all the variables

-6x+4x*x-20=0

Wy multiply elements

4x^2-6x-20=0

a = 4; b = -6; c = -20;
Δ = b2-4ac
Δ = -62-4·4·(-20)
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{89}}{2*4}=\frac{6-2\sqrt{89}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{89}}{2*4}=\frac{6+2\sqrt{89}}{8}
$