3a+(a^2/2)=8

Solution for 3a+(a^2/2)=8 equation:

3a+(a^2/2)=8

We move all terms to the left:

3a+(a^2/2)-(8)=0

We get rid of parentheses

a^2/2+3a-8=0

We multiply all the terms by the denominator


a^2+3a*2-8*2=0

We add all the numbers together, and all the variables

a^2+3a*2-16=0

Wy multiply elements

a^2+6a-16=0

a = 1; b = 6; c = -16;
Δ = b2-4ac
Δ = 62-4·1·(-16)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-10}{2*1}=\frac{-16}{2}
=-8
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+10}{2*1}=\frac{4}{2}
=2
$