12t+9=5t2

Solution for 12t+9=5t2 equation:

12t+9=5t^2

We move all terms to the left:

12t+9-(5t^2)=0

determiningTheFunctionDomain
-5t^2+12t+9=0

a = -5; b = 12; c = +9;
Δ = b2-4ac
Δ = 122-4·(-5)·9
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-18}{2*-5}=\frac{-30}{-10}
=+3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+18}{2*-5}=\frac{6}{-10}
=-3/5
$