(39/6x-12)+1=12/8x-16

Solution for (39/6x-12)+1=12/8x-16 equation:

(39/6x-12)+1=12/8x-16

We move all terms to the left:

(39/6x-12)+1-(12/8x-16)=0


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

x∈R



Domain of the equation: 8x-16)!=0

x∈R


We get rid of parentheses

39/6x-12/8x-12+16+1=0

We calculate fractions


312x/48x^2+(-72x)/48x^2-12+16+1=0

We add all the numbers together, and all the variables

312x/48x^2+(-72x)/48x^2+5=0

We multiply all the terms by the denominator


312x+(-72x)+5*48x^2=0

Wy multiply elements

240x^2+312x+(-72x)=0

We get rid of parentheses

240x^2+312x-72x=0

We add all the numbers together, and all the variables

240x^2+240x=0

a = 240; b = 240; c = 0;
Δ = b2-4ac
Δ = 2402-4·240·0
Δ = 57600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{57600}=240$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-240}{2*240}=\frac{-480}{480}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+240}{2*240}=\frac{0}{480}
=0
$