4x-1/5x+2=6

Solution for 4x-1/5x+2=6 equation:

4x-1/5x+2=6

We move all terms to the left:

4x-1/5x+2-(6)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

4x-1/5x-4=0

We multiply all the terms by the denominator


4x*5x-4*5x-1=0

Wy multiply elements

20x^2-20x-1=0

a = 20; b = -20; c = -1;
Δ = b2-4ac
Δ = -202-4·20·(-1)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{30}}{2*20}=\frac{20-4\sqrt{30}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{30}}{2*20}=\frac{20+4\sqrt{30}}{40}
$