12+5a=23(a)2

Solution for 12+5a=23(a)2 equation:

12+5a=23(a)2

We move all terms to the left:

12+5a-(23(a)2)=0

determiningTheFunctionDomain
5a-23a2+12=0

We add all the numbers together, and all the variables

-23a^2+5a+12=0

a = -23; b = 5; c = +12;
Δ = b2-4ac
Δ = 52-4·(-23)·12
Δ = 1129
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{1129}}{2*-23}=\frac{-5-\sqrt{1129}}{-46}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{1129}}{2*-23}=\frac{-5+\sqrt{1129}}{-46}
$