3a-4/2a+3=1

Solution for 3a-4/2a+3=1 equation:

3a-4/2a+3=1

We move all terms to the left:

3a-4/2a+3-(1)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We add all the numbers together, and all the variables

3a-4/2a+2=0

We multiply all the terms by the denominator


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

Wy multiply elements

6a^2+4a-4=0

a = 6; b = 4; c = -4;
Δ = b2-4ac
Δ = 42-4·6·(-4)
Δ = 112
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{7}}{2*6}=\frac{-4-4\sqrt{7}}{12}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{7}}{2*6}=\frac{-4+4\sqrt{7}}{12}
$