.5x-1=5/8x

Solution for .5x-1=5/8x equation:

.5x-1=5/8x

We move all terms to the left:

.5x-1-(5/8x)=0


Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

.5x-(+5/8x)-1=0

We get rid of parentheses

.5x-5/8x-1=0

We multiply all the terms by the denominator


(.5x)*8x-1*8x-5=0

We add all the numbers together, and all the variables

(+.5x)*8x-1*8x-5=0

We multiply parentheses

8x^2-1*8x-5=0

Wy multiply elements

8x^2-8x-5=0

a = 8; b = -8; c = -5;
Δ = b2-4ac
Δ = -82-4·8·(-5)
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{14}}{2*8}=\frac{8-4\sqrt{14}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{14}}{2*8}=\frac{8+4\sqrt{14}}{16}
$