3a+2/2a-4=0

Solution for 3a+2/2a-4=0 equation:

3a+2/2a-4=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We multiply all the terms by the denominator


3a*2a-4*2a+2=0

Wy multiply elements

6a^2-8a+2=0

a = 6; b = -8; c = +2;
Δ = b2-4ac
Δ = -82-4·6·2
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4}{2*6}=\frac{4}{12}
=1/3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4}{2*6}=\frac{12}{12}
=1
$