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

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

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

We move all terms to the left:

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


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

x∈R



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

x∈R


We multiply parentheses

10x-(3(1/3x-1))+15=0

We multiply all the terms by the denominator


10x*3x+15*3x-1))-(3(1-1))=0

We add all the numbers together, and all the variables

10x*3x+15*3x-1))-(30)=0

We add all the numbers together, and all the variables

10x*3x+15*3x=0

Wy multiply elements

30x^2+45x=0

a = 30; b = 45; c = 0;
Δ = b2-4ac
Δ = 452-4·30·0
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-45}{2*30}=\frac{-90}{60}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+45}{2*30}=\frac{0}{60}
=0
$