Y=9t^2-46t+48

Solution for Y=9t^2-46t+48 equation:

=9Y^2-46Y+48

We move all terms to the left:

-(9Y^2-46Y+48)=0

We get rid of parentheses

-9Y^2+46Y-48=0

a = -9; b = 46; c = -48;
Δ = b2-4ac
Δ = 462-4·(-9)·(-48)
Δ = 388
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-2\sqrt{97}}{2*-9}=\frac{-46-2\sqrt{97}}{-18}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+2\sqrt{97}}{2*-9}=\frac{-46+2\sqrt{97}}{-18}
$