X=8-6/8y

Solution for X=8-6/8y equation:

X=8-6/8X

We move all terms to the left:

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


Domain of the equation: 8X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

X+6/8X-8=0

We multiply all the terms by the denominator


X*8X-8*8X+6=0

Wy multiply elements

8X^2-64X+6=0

a = 8; b = -64; c = +6;
Δ = b2-4ac
Δ = -642-4·8·6
Δ = 3904
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:

$\sqrt{\Delta}=\sqrt{3904}=\sqrt{64*61}=\sqrt{64}*\sqrt{61}=8\sqrt{61}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-8\sqrt{61}}{2*8}=\frac{64-8\sqrt{61}}{16}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+8\sqrt{61}}{2*8}=\frac{64+8\sqrt{61}}{16}
$