13-1/4x=3x

Solution for 13-1/4x=3x equation:

13-1/4x=3x

We move all terms to the left:

13-1/4x-(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-1/4x+13=0

We multiply all the terms by the denominator


-3x*4x+13*4x-1=0

Wy multiply elements

-12x^2+52x-1=0

a = -12; b = 52; c = -1;
Δ = b2-4ac
Δ = 522-4·(-12)·(-1)
Δ = 2656
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:

$\sqrt{\Delta}=\sqrt{2656}=\sqrt{16*166}=\sqrt{16}*\sqrt{166}=4\sqrt{166}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-4\sqrt{166}}{2*-12}=\frac{-52-4\sqrt{166}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+4\sqrt{166}}{2*-12}=\frac{-52+4\sqrt{166}}{-24}
$