7/4x-3=2+9/2x

Solution for 7/4x-3=2+9/2x equation:

7/4x-3=2+9/2x

We move all terms to the left:

7/4x-3-(2+9/2x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

7/4x-(9/2x+2)-3=0

We get rid of parentheses

7/4x-9/2x-2-3=0

We calculate fractions


14x/8x^2+(-36x)/8x^2-2-3=0

We add all the numbers together, and all the variables

14x/8x^2+(-36x)/8x^2-5=0

We multiply all the terms by the denominator


14x+(-36x)-5*8x^2=0

Wy multiply elements

-40x^2+14x+(-36x)=0

We get rid of parentheses

-40x^2+14x-36x=0

We add all the numbers together, and all the variables

-40x^2-22x=0

a = -40; b = -22; c = 0;
Δ = b2-4ac
Δ = -222-4·(-40)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-22}{2*-40}=\frac{0}{-80}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+22}{2*-40}=\frac{44}{-80}
=-11/20
$