5/8x-12=0.5x

Solution for 5/8x-12=0.5x equation:

5/8x-12=0.5x

We move all terms to the left:

5/8x-12-(0.5x)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

5/8x-(+0.5x)-12=0

We get rid of parentheses

5/8x-0.5x-12=0

We multiply all the terms by the denominator


-(0.5x)*8x-12*8x+5=0

We add all the numbers together, and all the variables

-(+0.5x)*8x-12*8x+5=0

We multiply parentheses

-0x^2-12*8x+5=0

Wy multiply elements

-0x^2-96x+5=0

We add all the numbers together, and all the variables

-1x^2-96x+5=0

a = -1; b = -96; c = +5;
Δ = b2-4ac
Δ = -962-4·(-1)·5
Δ = 9236
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:

$\sqrt{\Delta}=\sqrt{9236}=\sqrt{4*2309}=\sqrt{4}*\sqrt{2309}=2\sqrt{2309}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-2\sqrt{2309}}{2*-1}=\frac{96-2\sqrt{2309}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+2\sqrt{2309}}{2*-1}=\frac{96+2\sqrt{2309}}{-2}
$