3t^2-15t=-12

Solution for 3t^2-15t=-12 equation:

3t^2-15t=-12

We move all terms to the left:

3t^2-15t-(-12)=0

We add all the numbers together, and all the variables

3t^2-15t+12=0

a = 3; b = -15; c = +12;
Δ = b2-4ac
Δ = -152-4·3·12
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-9}{2*3}=\frac{6}{6}
=1
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+9}{2*3}=\frac{24}{6}
=4
$