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

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

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

We move all terms to the left:

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


Domain of the equation: 2-a)!=0

We move all terms containing a to the left, all other terms to the right

-a)!=-2

a!=-2/1

a!=-2

a∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

3a^2+2a-1=0

a = 3; b = 2; c = -1;
Δ = b2-4ac
Δ = 22-4·3·(-1)
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{-(2)-4}{2*3}=\frac{-6}{6}
=-1
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4}{2*3}=\frac{2}{6}
=1/3
$