0=4t^2+9t-12

Solution for 0=4t^2+9t-12 equation:

0=4t^2+9t-12

We move all terms to the left:

0-(4t^2+9t-12)=0

We add all the numbers together, and all the variables

-(4t^2+9t-12)=0

We get rid of parentheses

-4t^2-9t+12=0

a = -4; b = -9; c = +12;
Δ = b2-4ac
Δ = -92-4·(-4)·12
Δ = 273
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{273}}{2*-4}=\frac{9-\sqrt{273}}{-8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{273}}{2*-4}=\frac{9+\sqrt{273}}{-8}
$