1/4+5/2x=7/3x

Solution for 1/4+5/2x=7/3x equation:

1/4+5/2x=7/3x

We move all terms to the left:

1/4+5/2x-(7/3x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5/2x-(+7/3x)+1/4=0

We get rid of parentheses

5/2x-7/3x+1/4=0

We calculate fractions


18x^2/96x^2+240x/96x^2+(-224x)/96x^2=0

We multiply all the terms by the denominator


18x^2+240x+(-224x)=0

We get rid of parentheses

18x^2+240x-224x=0

We add all the numbers together, and all the variables

18x^2+16x=0

a = 18; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·18·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*18}=\frac{-32}{36}
=-8/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*18}=\frac{0}{36}
=0
$