X+6=9/8x

Solution for X+6=9/8x equation:

X+6=9/8X

We move all terms to the left:

X+6-(9/8X)=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-(+9/8X)+6=0

We get rid of parentheses

X-9/8X+6=0

We multiply all the terms by the denominator


X*8X+6*8X-9=0

Wy multiply elements

8X^2+48X-9=0

a = 8; b = 48; c = -9;
Δ = b2-4ac
Δ = 482-4·8·(-9)
Δ = 2592
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:

$\sqrt{\Delta}=\sqrt{2592}=\sqrt{1296*2}=\sqrt{1296}*\sqrt{2}=36\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-36\sqrt{2}}{2*8}=\frac{-48-36\sqrt{2}}{16}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+36\sqrt{2}}{2*8}=\frac{-48+36\sqrt{2}}{16}
$