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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


(-180x^2)/48x^2+12x/48x^2+(-32x)/48x^2-1=0

We multiply all the terms by the denominator


(-180x^2)+12x+(-32x)-1*48x^2=0

Wy multiply elements

(-180x^2)-48x^2+12x+(-32x)=0

We get rid of parentheses

-180x^2-48x^2+12x-32x=0

We add all the numbers together, and all the variables

-228x^2-20x=0

a = -228; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·(-228)·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*-228}=\frac{0}{-456}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*-228}=\frac{40}{-456}
=-5/57
$