5t^2=12t+9

Solution for 5t^2=12t+9 equation:

5t^2=12t+9

We move all terms to the left:

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

We get rid of parentheses

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