Y=12n^2-42n

Solution for Y=12n^2-42n equation:

=12Y^2-42Y

We move all terms to the left:

-(12Y^2-42Y)=0

We get rid of parentheses

-12Y^2+42Y=0

a = -12; b = 42; c = 0;
Δ = b2-4ac
Δ = 422-4·(-12)·0
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-42}{2*-12}=\frac{-84}{-24}
=3+1/2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+42}{2*-12}=\frac{0}{-24}
=0
$