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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


48x^2/200x^2+50x/200x^2+(-300x)/200x^2+2=0

We multiply all the terms by the denominator


48x^2+50x+(-300x)+2*200x^2=0

Wy multiply elements

48x^2+400x^2+50x+(-300x)=0

We get rid of parentheses

48x^2+400x^2+50x-300x=0

We add all the numbers together, and all the variables

448x^2-250x=0

a = 448; b = -250; c = 0;
Δ = b2-4ac
Δ = -2502-4·448·0
Δ = 62500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{62500}=250$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-250)-250}{2*448}=\frac{0}{896}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-250)+250}{2*448}=\frac{500}{896}
=125/224
$