3a^2-5=-14a

Solution for 3a^2-5=-14a equation:

3a^2-5=-14a

We move all terms to the left:

3a^2-5-(-14a)=0

We get rid of parentheses

3a^2+14a-5=0

a = 3; b = 14; c = -5;
Δ = b2-4ac
Δ = 142-4·3·(-5)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-16}{2*3}=\frac{-30}{6}
=-5
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+16}{2*3}=\frac{2}{6}
=1/3
$