x/8x+2+3x+5=x+12

Solution for x/8x+2+3x+5=x+12 equation:

x/8x+2+3x+5=x+12

We move all terms to the left:

x/8x+2+3x+5-(x+12)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

3x+x/8x-(x+12)+7=0

We get rid of parentheses

3x+x/8x-x-12+7=0

We multiply all the terms by the denominator


3x*8x+x-x*8x-12*8x+7*8x=0

We add all the numbers together, and all the variables

x+3x*8x-x*8x-12*8x+7*8x=0

Wy multiply elements

24x^2-8x^2+x-96x+56x=0

We add all the numbers together, and all the variables

16x^2-39x=0

a = 16; b = -39; c = 0;
Δ = b2-4ac
Δ = -392-4·16·0
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-39}{2*16}=\frac{0}{32}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+39}{2*16}=\frac{78}{32}
=2+7/16
$