-1/4x+2=-3x-9

Solution for -1/4x+2=-3x-9 equation:

-1/4x+2=-3x-9

We move all terms to the left:

-1/4x+2-(-3x-9)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

-1/4x+3x+9+2=0

We multiply all the terms by the denominator


3x*4x+9*4x+2*4x-1=0

Wy multiply elements

12x^2+36x+8x-1=0

We add all the numbers together, and all the variables

12x^2+44x-1=0

a = 12; b = 44; c = -1;
Δ = b2-4ac
Δ = 442-4·12·(-1)
Δ = 1984
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:

$\sqrt{\Delta}=\sqrt{1984}=\sqrt{64*31}=\sqrt{64}*\sqrt{31}=8\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-8\sqrt{31}}{2*12}=\frac{-44-8\sqrt{31}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+8\sqrt{31}}{2*12}=\frac{-44+8\sqrt{31}}{24}
$