6+2/3x=-20-5x

Solution for 6+2/3x=-20-5x equation:

6+2/3x=-20-5x

We move all terms to the left:

6+2/3x-(-20-5x)=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-(-5x-20)+6=0

We get rid of parentheses

2/3x+5x+20+6=0

We multiply all the terms by the denominator


5x*3x+20*3x+6*3x+2=0

Wy multiply elements

15x^2+60x+18x+2=0

We add all the numbers together, and all the variables

15x^2+78x+2=0

a = 15; b = 78; c = +2;
Δ = b2-4ac
Δ = 782-4·15·2
Δ = 5964
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:

$\sqrt{\Delta}=\sqrt{5964}=\sqrt{4*1491}=\sqrt{4}*\sqrt{1491}=2\sqrt{1491}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-2\sqrt{1491}}{2*15}=\frac{-78-2\sqrt{1491}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+2\sqrt{1491}}{2*15}=\frac{-78+2\sqrt{1491}}{30}
$