4/x+9x-6x+4x=20

Solution for 4/x+9x-6x+4x=20 equation:

4/x+9x-6x+4x=20

We move all terms to the left:

4/x+9x-6x+4x-(20)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

7x+4/x-20=0

We multiply all the terms by the denominator


7x*x-20*x+4=0

We add all the numbers together, and all the variables

-20x+7x*x+4=0

Wy multiply elements

7x^2-20x+4=0

a = 7; b = -20; c = +4;
Δ = b2-4ac
Δ = -202-4·7·4
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-12\sqrt{2}}{2*7}=\frac{20-12\sqrt{2}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+12\sqrt{2}}{2*7}=\frac{20+12\sqrt{2}}{14}
$