X+6=11/8x

Solution for X+6=11/8x equation:

X+6=11/8X

We move all terms to the left:

X+6-(11/8X)=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-(+11/8X)+6=0

We get rid of parentheses

X-11/8X+6=0

We multiply all the terms by the denominator


X*8X+6*8X-11=0

Wy multiply elements

8X^2+48X-11=0

a = 8; b = 48; c = -11;
Δ = b2-4ac
Δ = 482-4·8·(-11)
Δ = 2656
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:

$\sqrt{\Delta}=\sqrt{2656}=\sqrt{16*166}=\sqrt{16}*\sqrt{166}=4\sqrt{166}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-4\sqrt{166}}{2*8}=\frac{-48-4\sqrt{166}}{16}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+4\sqrt{166}}{2*8}=\frac{-48+4\sqrt{166}}{16}
$