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

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

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

We move all terms to the left:

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


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

x∈R



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

x∈R


We multiply parentheses

6x-(2/3x-1)+6-5=0

We get rid of parentheses

6x-2/3x+1+6-5=0

We multiply all the terms by the denominator


6x*3x+1*3x+6*3x-5*3x-2=0

Wy multiply elements

18x^2+3x+18x-15x-2=0

We add all the numbers together, and all the variables

18x^2+6x-2=0

a = 18; b = 6; c = -2;
Δ = b2-4ac
Δ = 62-4·18·(-2)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{5}}{2*18}=\frac{-6-6\sqrt{5}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{5}}{2*18}=\frac{-6+6\sqrt{5}}{36}
$