-1/8x-14=x+4

Solution for -1/8x-14=x+4 equation:

-1/8x-14=x+4

We move all terms to the left:

-1/8x-14-(x+4)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We get rid of parentheses

-1/8x-x-4-14=0

We multiply all the terms by the denominator


-x*8x-4*8x-14*8x-1=0

Wy multiply elements

-8x^2-32x-112x-1=0

We add all the numbers together, and all the variables

-8x^2-144x-1=0

a = -8; b = -144; c = -1;
Δ = b2-4ac
Δ = -1442-4·(-8)·(-1)
Δ = 20704
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:

$\sqrt{\Delta}=\sqrt{20704}=\sqrt{16*1294}=\sqrt{16}*\sqrt{1294}=4\sqrt{1294}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-4\sqrt{1294}}{2*-8}=\frac{144-4\sqrt{1294}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+4\sqrt{1294}}{2*-8}=\frac{144+4\sqrt{1294}}{-16}
$