1-8/4x=46+x

Solution for 1-8/4x=46+x equation:

1-8/4x=46+x

We move all terms to the left:

1-8/4x-(46+x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-8/4x-(x+46)+1=0

We get rid of parentheses

-8/4x-x-46+1=0

We multiply all the terms by the denominator


-x*4x-46*4x+1*4x-8=0

Wy multiply elements

-4x^2-184x+4x-8=0

We add all the numbers together, and all the variables

-4x^2-180x-8=0

a = -4; b = -180; c = -8;
Δ = b2-4ac
Δ = -1802-4·(-4)·(-8)
Δ = 32272
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:

$\sqrt{\Delta}=\sqrt{32272}=\sqrt{16*2017}=\sqrt{16}*\sqrt{2017}=4\sqrt{2017}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-4\sqrt{2017}}{2*-4}=\frac{180-4\sqrt{2017}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+4\sqrt{2017}}{2*-4}=\frac{180+4\sqrt{2017}}{-8}
$