5+2/3x+3=-x+20

Solution for 5+2/3x+3=-x+20 equation:

5+2/3x+3=-x+20

We move all terms to the left:

5+2/3x+3-(-x+20)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(-1x+20)+5+3=0

We add all the numbers together, and all the variables

2/3x-(-1x+20)+8=0

We get rid of parentheses

2/3x+1x-20+8=0

We multiply all the terms by the denominator


1x*3x-20*3x+8*3x+2=0

Wy multiply elements

3x^2-60x+24x+2=0

We add all the numbers together, and all the variables

3x^2-36x+2=0

a = 3; b = -36; c = +2;
Δ = b2-4ac
Δ = -362-4·3·2
Δ = 1272
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:

$\sqrt{\Delta}=\sqrt{1272}=\sqrt{4*318}=\sqrt{4}*\sqrt{318}=2\sqrt{318}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-2\sqrt{318}}{2*3}=\frac{36-2\sqrt{318}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+2\sqrt{318}}{2*3}=\frac{36+2\sqrt{318}}{6}
$