5/2x-3/2x+5=9x-3

Solution for 5/2x-3/2x+5=9x-3 equation:

5/2x-3/2x+5=9x-3

We move all terms to the left:

5/2x-3/2x+5-(9x-3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

5/2x-3/2x-9x+3+5=0

We multiply all the terms by the denominator


-9x*2x+3*2x+5*2x+5-3=0

We add all the numbers together, and all the variables

-9x*2x+3*2x+5*2x+2=0

Wy multiply elements

-18x^2+6x+10x+2=0

We add all the numbers together, and all the variables

-18x^2+16x+2=0

a = -18; b = 16; c = +2;
Δ = b2-4ac
Δ = 162-4·(-18)·2
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{-(16)-20}{2*-18}=\frac{-36}{-36}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+20}{2*-18}=\frac{4}{-36}
=-1/9
$