-3t^2+10t=-30

Solution for -3t^2+10t=-30 equation:

-3t^2+10t=-30

We move all terms to the left:

-3t^2+10t-(-30)=0

We add all the numbers together, and all the variables

-3t^2+10t+30=0

a = -3; b = 10; c = +30;
Δ = b2-4ac
Δ = 102-4·(-3)·30
Δ = 460
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:

$\sqrt{\Delta}=\sqrt{460}=\sqrt{4*115}=\sqrt{4}*\sqrt{115}=2\sqrt{115}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{115}}{2*-3}=\frac{-10-2\sqrt{115}}{-6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{115}}{2*-3}=\frac{-10+2\sqrt{115}}{-6}
$