-4/3x+16=-2x+20

Solution for -4/3x+16=-2x+20 equation:

-4/3x+16=-2x+20

We move all terms to the left:

-4/3x+16-(-2x+20)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

-4/3x+2x-20+16=0

We multiply all the terms by the denominator


2x*3x-20*3x+16*3x-4=0

Wy multiply elements

6x^2-60x+48x-4=0

We add all the numbers together, and all the variables

6x^2-12x-4=0

a = 6; b = -12; c = -4;
Δ = b2-4ac
Δ = -122-4·6·(-4)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{15}}{2*6}=\frac{12-4\sqrt{15}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{15}}{2*6}=\frac{12+4\sqrt{15}}{12}
$