a-3a^2=-8

Solution for a-3a^2=-8 equation:

a-3a^2=-8

We move all terms to the left:

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

We add all the numbers together, and all the variables

-3a^2+a+8=0

a = -3; b = 1; c = +8;
Δ = b2-4ac
Δ = 12-4·(-3)·8
Δ = 97
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{-(1)-\sqrt{97}}{2*-3}=\frac{-1-\sqrt{97}}{-6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{97}}{2*-3}=\frac{-1+\sqrt{97}}{-6}
$