4(3x+1)=8/16x-36

Solution for 4(3x+1)=8/16x-36 equation:

4(3x+1)=8/16x-36

We move all terms to the left:

4(3x+1)-(8/16x-36)=0


Domain of the equation: 16x-36)!=0

x∈R


We multiply parentheses

12x-(8/16x-36)+4=0

We get rid of parentheses

12x-8/16x+36+4=0

We multiply all the terms by the denominator


12x*16x+36*16x+4*16x-8=0

Wy multiply elements

192x^2+576x+64x-8=0

We add all the numbers together, and all the variables

192x^2+640x-8=0

a = 192; b = 640; c = -8;
Δ = b2-4ac
Δ = 6402-4·192·(-8)
Δ = 415744
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:

$\sqrt{\Delta}=\sqrt{415744}=\sqrt{1024*406}=\sqrt{1024}*\sqrt{406}=32\sqrt{406}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(640)-32\sqrt{406}}{2*192}=\frac{-640-32\sqrt{406}}{384}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(640)+32\sqrt{406}}{2*192}=\frac{-640+32\sqrt{406}}{384}
$