2(a-1)+3a^2+3a/3a-1=14

Solution for 2(a-1)+3a^2+3a/3a-1=14 equation:

2(a-1)+3a^2+3a/3a-1=14

We move all terms to the left:

2(a-1)+3a^2+3a/3a-1-(14)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R


We add all the numbers together, and all the variables

3a^2+2(a-1)+3a/3a-15=0

We multiply parentheses

3a^2+2a+3a/3a-2-15=0

Fractions to decimals

3a^2+2a-2-15+1=0

We add all the numbers together, and all the variables

3a^2+2a-16=0

a = 3; b = 2; c = -16;
Δ = b2-4ac
Δ = 22-4·3·(-16)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-14}{2*3}=\frac{-16}{6}
=-2+2/3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+14}{2*3}=\frac{12}{6}
=2
$