5a^2-9=116

Solution for 5a^2-9=116 equation:

5a^2-9=116

We move all terms to the left:

5a^2-9-(116)=0

We add all the numbers together, and all the variables

5a^2-125=0

a = 5; b = 0; c = -125;
Δ = b2-4ac
Δ = 02-4·5·(-125)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-50}{2*5}=\frac{-50}{10}
=-5
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+50}{2*5}=\frac{50}{10}
=5
$