4x+16=2/3x+2

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

4x+16=2/3x+2

We move all terms to the left:

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


Domain of the equation: 3x+2)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

12x^2+42x-2=0

a = 12; b = 42; c = -2;
Δ = b2-4ac
Δ = 422-4·12·(-2)
Δ = 1860
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:

$\sqrt{\Delta}=\sqrt{1860}=\sqrt{4*465}=\sqrt{4}*\sqrt{465}=2\sqrt{465}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{465}}{2*12}=\frac{-42-2\sqrt{465}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{465}}{2*12}=\frac{-42+2\sqrt{465}}{24}
$