9/4x+6=12x

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

9/4x+6=12x

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-48x^2+24x+9=0

a = -48; b = 24; c = +9;
Δ = b2-4ac
Δ = 242-4·(-48)·9
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-48}{2*-48}=\frac{-72}{-96}
=3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+48}{2*-48}=\frac{24}{-96}
=-1/4
$