5/2x+7/4=3+7/6x

Solution for 5/2x+7/4=3+7/6x equation:

5/2x+7/4=3+7/6x

We move all terms to the left:

5/2x+7/4-(3+7/6x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5/2x-(7/6x+3)+7/4=0

We get rid of parentheses

5/2x-7/6x-3+7/4=0

We calculate fractions


504x^2/192x^2+480x/192x^2+(-224x)/192x^2-3=0

We multiply all the terms by the denominator


504x^2+480x+(-224x)-3*192x^2=0

Wy multiply elements

504x^2-576x^2+480x+(-224x)=0

We get rid of parentheses

504x^2-576x^2+480x-224x=0

We add all the numbers together, and all the variables

-72x^2+256x=0

a = -72; b = 256; c = 0;
Δ = b2-4ac
Δ = 2562-4·(-72)·0
Δ = 65536
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{65536}=256$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(256)-256}{2*-72}=\frac{-512}{-144}
=3+5/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(256)+256}{2*-72}=\frac{0}{-144}
=0
$