2a-4/3a+4=0

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

2a-4/3a+4=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R


We multiply all the terms by the denominator


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

Wy multiply elements

6a^2+12a-4=0

a = 6; b = 12; c = -4;
Δ = b2-4ac
Δ = 122-4·6·(-4)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{15}}{2*6}=\frac{-12-4\sqrt{15}}{12}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{15}}{2*6}=\frac{-12+4\sqrt{15}}{12}
$