1/4x-28=1+3x

Solution for 1/4x-28=1+3x equation:

1/4x-28=1+3x

We move all terms to the left:

1/4x-28-(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

1/4x-(3x+1)-28=0

We get rid of parentheses

1/4x-3x-1-28=0

We multiply all the terms by the denominator


-3x*4x-1*4x-28*4x+1=0

Wy multiply elements

-12x^2-4x-112x+1=0

We add all the numbers together, and all the variables

-12x^2-116x+1=0

a = -12; b = -116; c = +1;
Δ = b2-4ac
Δ = -1162-4·(-12)·1
Δ = 13504
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:

$\sqrt{\Delta}=\sqrt{13504}=\sqrt{64*211}=\sqrt{64}*\sqrt{211}=8\sqrt{211}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-116)-8\sqrt{211}}{2*-12}=\frac{116-8\sqrt{211}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-116)+8\sqrt{211}}{2*-12}=\frac{116+8\sqrt{211}}{-24}
$