6a^2-a-97=3

Solution for 6a^2-a-97=3 equation:

6a^2-a-97=3

We move all terms to the left:

6a^2-a-97-(3)=0

We add all the numbers together, and all the variables

6a^2-1a-100=0

a = 6; b = -1; c = -100;
Δ = b2-4ac
Δ = -12-4·6·(-100)
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-49}{2*6}=\frac{-48}{12}
=-4
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+49}{2*6}=\frac{50}{12}
=4+1/6
$