2(1/3x-3)+2=4/5x-2

Solution for 2(1/3x-3)+2=4/5x-2 equation:

2(1/3x-3)+2=4/5x-2

We move all terms to the left:

2(1/3x-3)+2-(4/5x-2)=0


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

x∈R



Domain of the equation: 5x-2)!=0

x∈R


We multiply parentheses

2x-(4/5x-2)-6+2=0

We get rid of parentheses

2x-4/5x+2-6+2=0

We multiply all the terms by the denominator


2x*5x+2*5x-6*5x+2*5x-4=0

Wy multiply elements

10x^2+10x-30x+10x-4=0

We add all the numbers together, and all the variables

10x^2-10x-4=0

a = 10; b = -10; c = -4;
Δ = b2-4ac
Δ = -102-4·10·(-4)
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{65}}{2*10}=\frac{10-2\sqrt{65}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{65}}{2*10}=\frac{10+2\sqrt{65}}{20}
$