2x-4=5+2/3x+16

Solution for 2x-4=5+2/3x+16 equation:

2x-4=5+2/3x+16

We move all terms to the left:

2x-4-(5+2/3x+16)=0


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

x∈R


We add all the numbers together, and all the variables

2x-(2/3x+21)-4=0

We get rid of parentheses

2x-2/3x-21-4=0

We multiply all the terms by the denominator


2x*3x-21*3x-4*3x-2=0

Wy multiply elements

6x^2-63x-12x-2=0

We add all the numbers together, and all the variables

6x^2-75x-2=0

a = 6; b = -75; c = -2;
Δ = b2-4ac
Δ = -752-4·6·(-2)
Δ = 5673
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-\sqrt{5673}}{2*6}=\frac{75-\sqrt{5673}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+\sqrt{5673}}{2*6}=\frac{75+\sqrt{5673}}{12}
$