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

Solution for 2(3/5x+3)-(2/3x-1)= equation:

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

We move all terms to the left:

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


Domain of the equation: 5x+3)!=0

x∈R



Domain of the equation: 3x-1)!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

6x-(2/3x-1)+6=0

We get rid of parentheses

6x-2/3x+1+6=0

We multiply all the terms by the denominator


6x*3x+1*3x+6*3x-2=0

Wy multiply elements

18x^2+3x+18x-2=0

We add all the numbers together, and all the variables

18x^2+21x-2=0

a = 18; b = 21; c = -2;
Δ = b2-4ac
Δ = 212-4·18·(-2)
Δ = 585
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:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{65}}{2*18}=\frac{-21-3\sqrt{65}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{65}}{2*18}=\frac{-21+3\sqrt{65}}{36}
$