7/8x+9=x

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

7/8x+9=x

We move all terms to the left:

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


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+7/8x+9=0

We multiply all the terms by the denominator


-1x*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}
$