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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x+3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


64x^2/200x^2+(-300x)/200x^2+(-150x)/200x^2-3=0

We multiply all the terms by the denominator


64x^2+(-300x)+(-150x)-3*200x^2=0

Wy multiply elements

64x^2-600x^2+(-300x)+(-150x)=0

We get rid of parentheses

64x^2-600x^2-300x-150x=0

We add all the numbers together, and all the variables

-536x^2-450x=0

a = -536; b = -450; c = 0;
Δ = b2-4ac
Δ = -4502-4·(-536)·0
Δ = 202500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{202500}=450$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-450)-450}{2*-536}=\frac{0}{-1072}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-450)+450}{2*-536}=\frac{900}{-1072}
=-225/268
$