x=8x+1/2x-6

Solution for x=8x+1/2x-6 equation:

x=8x+1/2x-6

We move all terms to the left:

x-(8x+1/2x-6)=0


Domain of the equation: 2x-6)!=0

x∈R


We get rid of parentheses

x-8x-1/2x+6=0

We multiply all the terms by the denominator


x*2x-8x*2x+6*2x-1=0

Wy multiply elements

2x^2-16x^2+12x-1=0

We add all the numbers together, and all the variables

-14x^2+12x-1=0

a = -14; b = 12; c = -1;
Δ = b2-4ac
Δ = 122-4·(-14)·(-1)
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{22}}{2*-14}=\frac{-12-2\sqrt{22}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{22}}{2*-14}=\frac{-12+2\sqrt{22}}{-28}
$