1/5x+3x+x=12

Solution for 1/5x+3x+x=12 equation:

1/5x+3x+x=12

We move all terms to the left:

1/5x+3x+x-(12)=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-12=0

We multiply all the terms by the denominator


4x*5x-12*5x+1=0

Wy multiply elements

20x^2-60x+1=0

a = 20; b = -60; c = +1;
Δ = b2-4ac
Δ = -602-4·20·1
Δ = 3520
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:

$\sqrt{\Delta}=\sqrt{3520}=\sqrt{64*55}=\sqrt{64}*\sqrt{55}=8\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-8\sqrt{55}}{2*20}=\frac{60-8\sqrt{55}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+8\sqrt{55}}{2*20}=\frac{60+8\sqrt{55}}{40}
$