5/2x-1=12x

Solution for 5/2x-1=12x equation:

5/2x-1=12x

We move all terms to the left:

5/2x-1-(12x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-12x+5/2x-1=0

We multiply all the terms by the denominator


-12x*2x-1*2x+5=0

Wy multiply elements

-24x^2-2x+5=0

a = -24; b = -2; c = +5;
Δ = b2-4ac
Δ = -22-4·(-24)·5
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-22}{2*-24}=\frac{-20}{-48}
=5/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+22}{2*-24}=\frac{24}{-48}
=-1/2
$