9/4x-1=3x

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

9/4x-1=3x

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-12x^2-4x+9=0

a = -12; b = -4; c = +9;
Δ = b2-4ac
Δ = -42-4·(-12)·9
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8\sqrt{7}}{2*-12}=\frac{4-8\sqrt{7}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8\sqrt{7}}{2*-12}=\frac{4+8\sqrt{7}}{-24}
$