Y=x^2-x-306

Solution for Y=x^2-x-306 equation:

=Y^2-Y-306

We move all terms to the left:

-(Y^2-Y-306)=0

We get rid of parentheses

-Y^2+Y+306=0

We add all the numbers together, and all the variables

-1Y^2+Y+306=0

a = -1; b = 1; c = +306;
Δ = b2-4ac
Δ = 12-4·(-1)·306
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-35}{2*-1}=\frac{-36}{-2}
=+18
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+35}{2*-1}=\frac{34}{-2}
=-17
$