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

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

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

We move all terms to the left:

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

We multiply parentheses

3a^2+8a-((3a+8))-24=0


We calculate terms in parentheses: -((3a+8)), so:

(3a+8)

We get rid of parentheses

3a+8

Back to the equation:

-(3a+8)


We get rid of parentheses

3a^2+8a-3a-8-24=0

We add all the numbers together, and all the variables

3a^2+5a-32=0

a = 3; b = 5; c = -32;
Δ = b2-4ac
Δ = 52-4·3·(-32)
Δ = 409
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{-(5)-\sqrt{409}}{2*3}=\frac{-5-\sqrt{409}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{409}}{2*3}=\frac{-5+\sqrt{409}}{6}
$