t^2-30*t-30=0

Solution for t^2-30*t-30=0 equation:

t^2-30t-30=0

a = 1; b = -30; c = -30;
Δ = b2-4ac
Δ = -302-4·1·(-30)
Δ = 1020
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:

$\sqrt{\Delta}=\sqrt{1020}=\sqrt{4*255}=\sqrt{4}*\sqrt{255}=2\sqrt{255}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{255}}{2*1}=\frac{30-2\sqrt{255}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{255}}{2*1}=\frac{30+2\sqrt{255}}{2}
$