-12x+6=9-1/4x

Solution for -12x+6=9-1/4x equation:

-12x+6=9-1/4x

We move all terms to the left:

-12x+6-(9-1/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-12x-(-1/4x+9)+6=0

We get rid of parentheses

-12x+1/4x-9+6=0

We multiply all the terms by the denominator


-12x*4x-9*4x+6*4x+1=0

Wy multiply elements

-48x^2-36x+24x+1=0

We add all the numbers together, and all the variables

-48x^2-12x+1=0

a = -48; b = -12; c = +1;
Δ = b2-4ac
Δ = -122-4·(-48)·1
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{21}}{2*-48}=\frac{12-4\sqrt{21}}{-96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{21}}{2*-48}=\frac{12+4\sqrt{21}}{-96}
$