1/5x=6x-2

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

1/5x=6x-2

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

1/5x-6x+2=0

We multiply all the terms by the denominator


-6x*5x+2*5x+1=0

Wy multiply elements

-30x^2+10x+1=0

a = -30; b = 10; c = +1;
Δ = b2-4ac
Δ = 102-4·(-30)·1
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{55}}{2*-30}=\frac{-10-2\sqrt{55}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{55}}{2*-30}=\frac{-10+2\sqrt{55}}{-60}
$