1/5x+2=3x

Solution for 1/5x+2=3x equation:

1/5x+2=3x

We move all terms to the left:

1/5x+2-(3x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-3x+1/5x+2=0

We multiply all the terms by the denominator


-3x*5x+2*5x+1=0

Wy multiply elements

-15x^2+10x+1=0

a = -15; b = 10; c = +1;
Δ = b2-4ac
Δ = 102-4·(-15)·1
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4\sqrt{10}}{2*-15}=\frac{-10-4\sqrt{10}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4\sqrt{10}}{2*-15}=\frac{-10+4\sqrt{10}}{-30}
$