2x-4=52/3x+16

Solution for 2x-4=52/3x+16 equation:

2x-4=52/3x+16

We move all terms to the left:

2x-4-(52/3x+16)=0


Domain of the equation: 3x+16)!=0

x∈R


We get rid of parentheses

2x-52/3x-16-4=0

We multiply all the terms by the denominator


2x*3x-16*3x-4*3x-52=0

Wy multiply elements

6x^2-48x-12x-52=0

We add all the numbers together, and all the variables

6x^2-60x-52=0

a = 6; b = -60; c = -52;
Δ = b2-4ac
Δ = -602-4·6·(-52)
Δ = 4848
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:

$\sqrt{\Delta}=\sqrt{4848}=\sqrt{16*303}=\sqrt{16}*\sqrt{303}=4\sqrt{303}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{303}}{2*6}=\frac{60-4\sqrt{303}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{303}}{2*6}=\frac{60+4\sqrt{303}}{12}
$