x-9=7/8x

Solution for x-9=7/8x equation:

x-9=7/8x

We move all terms to the left:

x-9-(7/8x)=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-(+7/8x)-9=0

We get rid of parentheses

x-7/8x-9=0

We multiply all the terms by the denominator


x*8x-9*8x-7=0

Wy multiply elements

8x^2-72x-7=0

a = 8; b = -72; c = -7;
Δ = b2-4ac
Δ = -722-4·8·(-7)
Δ = 5408
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:

$\sqrt{\Delta}=\sqrt{5408}=\sqrt{2704*2}=\sqrt{2704}*\sqrt{2}=52\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-52\sqrt{2}}{2*8}=\frac{72-52\sqrt{2}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+52\sqrt{2}}{2*8}=\frac{72+52\sqrt{2}}{16}
$