1/5x+2=3x-6+6x

Solution for 1/5x+2=3x-6+6x equation:

1/5x+2=3x-6+6x

We move all terms to the left:

1/5x+2-(3x-6+6x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

1/5x-(9x-6)+2=0

We get rid of parentheses

1/5x-9x+6+2=0

We multiply all the terms by the denominator


-9x*5x+6*5x+2*5x+1=0

Wy multiply elements

-45x^2+30x+10x+1=0

We add all the numbers together, and all the variables

-45x^2+40x+1=0

a = -45; b = 40; c = +1;
Δ = b2-4ac
Δ = 402-4·(-45)·1
Δ = 1780
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:

$\sqrt{\Delta}=\sqrt{1780}=\sqrt{4*445}=\sqrt{4}*\sqrt{445}=2\sqrt{445}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{445}}{2*-45}=\frac{-40-2\sqrt{445}}{-90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{445}}{2*-45}=\frac{-40+2\sqrt{445}}{-90}
$