Y=3t^2-7t-12

Solution for Y=3t^2-7t-12 equation:

=3Y^2-7Y-12

We move all terms to the left:

-(3Y^2-7Y-12)=0

We get rid of parentheses

-3Y^2+7Y+12=0

a = -3; b = 7; c = +12;
Δ = b2-4ac
Δ = 72-4·(-3)·12
Δ = 193
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{193}}{2*-3}=\frac{-7-\sqrt{193}}{-6}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{193}}{2*-3}=\frac{-7+\sqrt{193}}{-6}
$