-5+1/4x=3x+1

Solution for -5+1/4x=3x+1 equation:

-5+1/4x=3x+1

We move all terms to the left:

-5+1/4x-(3x+1)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x-3x-1-5=0

We multiply all the terms by the denominator


-3x*4x-1*4x-5*4x+1=0

Wy multiply elements

-12x^2-4x-20x+1=0

We add all the numbers together, and all the variables

-12x^2-24x+1=0

a = -12; b = -24; c = +1;
Δ = b2-4ac
Δ = -242-4·(-12)·1
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{39}}{2*-12}=\frac{24-4\sqrt{39}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{39}}{2*-12}=\frac{24+4\sqrt{39}}{-24}
$