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

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

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

We move all terms to the left:

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


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 3x-2)!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

-10x-(1/3x-2)+5=0

We get rid of parentheses

-10x-1/3x+2+5=0

We multiply all the terms by the denominator


-10x*3x+2*3x+5*3x-1=0

Wy multiply elements

-30x^2+6x+15x-1=0

We add all the numbers together, and all the variables

-30x^2+21x-1=0

a = -30; b = 21; c = -1;
Δ = b2-4ac
Δ = 212-4·(-30)·(-1)
Δ = 321
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-\sqrt{321}}{2*-30}=\frac{-21-\sqrt{321}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{321}}{2*-30}=\frac{-21+\sqrt{321}}{-60}
$