2a-4/3a+4=1

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

2a-4/3a+4=1

We move all terms to the left:

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


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R


We add all the numbers together, and all the variables

2a-4/3a+3=0

We multiply all the terms by the denominator


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

Wy multiply elements

6a^2+9a-4=0

a = 6; b = 9; c = -4;
Δ = b2-4ac
Δ = 92-4·6·(-4)
Δ = 177
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{177}}{2*6}=\frac{-9-\sqrt{177}}{12}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{177}}{2*6}=\frac{-9+\sqrt{177}}{12}
$