X+6/2x-8=6

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

X+6/2X-8=6

We move all terms to the left:

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


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We add all the numbers together, and all the variables

X+6/2X-14=0

We multiply all the terms by the denominator


X*2X-14*2X+6=0

Wy multiply elements

2X^2-28X+6=0

a = 2; b = -28; c = +6;
Δ = b2-4ac
Δ = -282-4·2·6
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{46}}{2*2}=\frac{28-4\sqrt{46}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{46}}{2*2}=\frac{28+4\sqrt{46}}{4}
$