1-8/14x=46+x

Solution for 1-8/14x=46+x equation:

1-8/14x=46+x

We move all terms to the left:

1-8/14x-(46+x)=0


Domain of the equation: 14x!=0

x!=0/14

x!=0

x∈R


We add all the numbers together, and all the variables

-8/14x-(x+46)+1=0

We get rid of parentheses

-8/14x-x-46+1=0

We multiply all the terms by the denominator


-x*14x-46*14x+1*14x-8=0

Wy multiply elements

-14x^2-644x+14x-8=0

We add all the numbers together, and all the variables

-14x^2-630x-8=0

a = -14; b = -630; c = -8;
Δ = b2-4ac
Δ = -6302-4·(-14)·(-8)
Δ = 396452
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:

$\sqrt{\Delta}=\sqrt{396452}=\sqrt{4*99113}=\sqrt{4}*\sqrt{99113}=2\sqrt{99113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-630)-2\sqrt{99113}}{2*-14}=\frac{630-2\sqrt{99113}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-630)+2\sqrt{99113}}{2*-14}=\frac{630+2\sqrt{99113}}{-28}
$