5/8x+4=3/6x+12

Solution for 5/8x+4=3/6x+12 equation:

5/8x+4=3/6x+12

We move all terms to the left:

5/8x+4-(3/6x+12)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 6x+12)!=0

x∈R


We get rid of parentheses

5/8x-3/6x-12+4=0

We calculate fractions


30x/48x^2+(-24x)/48x^2-12+4=0

We add all the numbers together, and all the variables

30x/48x^2+(-24x)/48x^2-8=0

We multiply all the terms by the denominator


30x+(-24x)-8*48x^2=0

Wy multiply elements

-384x^2+30x+(-24x)=0

We get rid of parentheses

-384x^2+30x-24x=0

We add all the numbers together, and all the variables

-384x^2+6x=0

a = -384; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-384)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-384}=\frac{-12}{-768}
=1/64
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-384}=\frac{0}{-768}
=0
$