8.5=2+3x+1/8x

Solution for 8.5=2+3x+1/8x equation:

8.5=2+3x+1/8x

We move all terms to the left:

8.5-(2+3x+1/8x)=0


Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(3x+1/8x+2)+8.5=0

We get rid of parentheses

-3x-1/8x-2+8.5=0

We multiply all the terms by the denominator


-3x*8x-2*8x+(8.5)*8x-1=0

We multiply parentheses

-3x*8x-2*8x+68x-1=0

Wy multiply elements

-24x^2-16x+68x-1=0

We add all the numbers together, and all the variables

-24x^2+52x-1=0

a = -24; b = 52; c = -1;
Δ = b2-4ac
Δ = 522-4·(-24)·(-1)
Δ = 2608
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:

$\sqrt{\Delta}=\sqrt{2608}=\sqrt{16*163}=\sqrt{16}*\sqrt{163}=4\sqrt{163}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-4\sqrt{163}}{2*-24}=\frac{-52-4\sqrt{163}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+4\sqrt{163}}{2*-24}=\frac{-52+4\sqrt{163}}{-48}
$