5-0.5x=5/8x+2

Solution for 5-0.5x=5/8x+2 equation:

5-0.5x=5/8x+2

We move all terms to the left:

5-0.5x-(5/8x+2)=0


Domain of the equation: 8x+2)!=0

x∈R


We get rid of parentheses

-0.5x-5/8x-2+5=0

We multiply all the terms by the denominator


-(0.5x)*8x-2*8x+5*8x-5=0

We add all the numbers together, and all the variables

-(+0.5x)*8x-2*8x+5*8x-5=0

We multiply parentheses

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

Wy multiply elements

-0x^2-16x+40x-5=0

We add all the numbers together, and all the variables

-1x^2+24x-5=0

a = -1; b = 24; c = -5;
Δ = b2-4ac
Δ = 242-4·(-1)·(-5)
Δ = 556
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:

$\sqrt{\Delta}=\sqrt{556}=\sqrt{4*139}=\sqrt{4}*\sqrt{139}=2\sqrt{139}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{139}}{2*-1}=\frac{-24-2\sqrt{139}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{139}}{2*-1}=\frac{-24+2\sqrt{139}}{-2}
$