8x-5/2x=2.5

Solution for 8x-5/2x=2.5 equation:

8x-5/2x=2.5

We move all terms to the left:

8x-5/2x-(2.5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

8x-5/2x-2.5=0

We multiply all the terms by the denominator


8x*2x-(2.5)*2x-5=0

We multiply parentheses

8x*2x-5x-5=0

Wy multiply elements

16x^2-5x-5=0

a = 16; b = -5; c = -5;
Δ = b2-4ac
Δ = -52-4·16·(-5)
Δ = 345
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{345}}{2*16}=\frac{5-\sqrt{345}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{345}}{2*16}=\frac{5+\sqrt{345}}{32}
$