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 = 6204
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:

$\sqrt{\Delta}=\sqrt{6204}=\sqrt{4*1551}=\sqrt{4}*\sqrt{1551}=2\sqrt{1551}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-2\sqrt{1551}}{2*-15}=\frac{-78-2\sqrt{1551}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+2\sqrt{1551}}{2*-15}=\frac{-78+2\sqrt{1551}}{-30}
$