2a-5=3/2a-3

Solution for 2a-5=3/2a-3 equation:

2a-5=3/2a-3

We move all terms to the left:

2a-5-(3/2a-3)=0


Domain of the equation: 2a-3)!=0

a∈R


We get rid of parentheses

2a-3/2a+3-5=0

We multiply all the terms by the denominator


2a*2a+3*2a-5*2a-3=0

Wy multiply elements

4a^2+6a-10a-3=0

We add all the numbers together, and all the variables

4a^2-4a-3=0

a = 4; b = -4; c = -3;
Δ = b2-4ac
Δ = -42-4·4·(-3)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8}{2*4}=\frac{-4}{8}
=-1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8}{2*4}=\frac{12}{8}
=1+1/2
$