1/4x+2=-1-6x

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

1/4x+2=-1-6x

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/4x+6x+1+2=0

We multiply all the terms by the denominator


6x*4x+1*4x+2*4x+1=0

Wy multiply elements

24x^2+4x+8x+1=0

We add all the numbers together, and all the variables

24x^2+12x+1=0

a = 24; b = 12; c = +1;
Δ = b2-4ac
Δ = 122-4·24·1
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{3}}{2*24}=\frac{-12-4\sqrt{3}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{3}}{2*24}=\frac{-12+4\sqrt{3}}{48}
$