x=6x-2/2x+8

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

x=6x-2/2x+8

We move all terms to the left:

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


Domain of the equation: 2x+8)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-10x^2-16x+2=0

a = -10; b = -16; c = +2;
Δ = b2-4ac
Δ = -162-4·(-10)·2
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{21}}{2*-10}=\frac{16-4\sqrt{21}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{21}}{2*-10}=\frac{16+4\sqrt{21}}{-20}
$