15t^2-27t=6

Solution for 15t^2-27t=6 equation:

15t^2-27t=6

We move all terms to the left:

15t^2-27t-(6)=0

a = 15; b = -27; c = -6;
Δ = b2-4ac
Δ = -272-4·15·(-6)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-33}{2*15}=\frac{-6}{30}
=-1/5
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+33}{2*15}=\frac{60}{30}
=2
$