2=x-7/8x

Solution for 2=x-7/8x equation:

2=x-7/8x

We move all terms to the left:

2-(x-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)+2=0

We get rid of parentheses

-x+7/8x+2=0

We multiply all the terms by the denominator


-x*8x+2*8x+7=0

Wy multiply elements

-8x^2+16x+7=0

a = -8; b = 16; c = +7;
Δ = b2-4ac
Δ = 162-4·(-8)·7
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{30}}{2*-8}=\frac{-16-4\sqrt{30}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{30}}{2*-8}=\frac{-16+4\sqrt{30}}{-16}
$