Y=12m^2+74m+90

Solution for Y=12m^2+74m+90 equation:

=12Y^2+74Y+90

We move all terms to the left:

-(12Y^2+74Y+90)=0

We get rid of parentheses

-12Y^2-74Y-90=0

a = -12; b = -74; c = -90;
Δ = b2-4ac
Δ = -742-4·(-12)·(-90)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-74)-34}{2*-12}=\frac{40}{-24}
=-1+2/3
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-74)+34}{2*-12}=\frac{108}{-24}
=-4+1/2
$