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

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

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

We move all terms to the left:

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


Domain of the equation: 4x+2)!=0

x∈R



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

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

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

We multiply all the terms by the denominator


2x*5x)-3)-(3(+4*5x)-3)+2=0

Wy multiply elements

10x^2+20x=0

a = 10; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·10·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*10}=\frac{-40}{20}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*10}=\frac{0}{20}
=0
$