0=5t^2+30t-45

Solution for 0=5t^2+30t-45 equation:

0=5t^2+30t-45

We move all terms to the left:

0-(5t^2+30t-45)=0

We add all the numbers together, and all the variables

-(5t^2+30t-45)=0

We get rid of parentheses

-5t^2-30t+45=0

a = -5; b = -30; c = +45;
Δ = b2-4ac
Δ = -302-4·(-5)·45
Δ = 1800
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:

$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30\sqrt{2}}{2*-5}=\frac{30-30\sqrt{2}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30\sqrt{2}}{2*-5}=\frac{30+30\sqrt{2}}{-10}
$