30t-2=-27-3t^2

Solution for 30t-2=-27-3t^2 equation:

30t-2=-27-3t^2

We move all terms to the left:

30t-2-(-27-3t^2)=0

We get rid of parentheses

3t^2+30t+27-2=0

We add all the numbers together, and all the variables

3t^2+30t+25=0

a = 3; b = 30; c = +25;
Δ = b2-4ac
Δ = 302-4·3·25
Δ = 600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-10\sqrt{6}}{2*3}=\frac{-30-10\sqrt{6}}{6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+10\sqrt{6}}{2*3}=\frac{-30+10\sqrt{6}}{6}
$