7/8x-8=x

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

7/8x-8=x

We move all terms to the left:

7/8x-8-(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-8=0

We multiply all the terms by the denominator


-1x*8x-8*8x+7=0

Wy multiply elements

-8x^2-64x+7=0

a = -8; b = -64; c = +7;
Δ = b2-4ac
Δ = -642-4·(-8)·7
Δ = 4320
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:

$\sqrt{\Delta}=\sqrt{4320}=\sqrt{144*30}=\sqrt{144}*\sqrt{30}=12\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-12\sqrt{30}}{2*-8}=\frac{64-12\sqrt{30}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+12\sqrt{30}}{2*-8}=\frac{64+12\sqrt{30}}{-16}
$