5t^2-20t-30=0

Solution for 5t^2-20t-30=0 equation:

5t^2-20t-30=0

a = 5; b = -20; c = -30;
Δ = b2-4ac
Δ = -202-4·5·(-30)
Δ = 1000
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:

$\sqrt{\Delta}=\sqrt{1000}=\sqrt{100*10}=\sqrt{100}*\sqrt{10}=10\sqrt{10}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-10\sqrt{10}}{2*5}=\frac{20-10\sqrt{10}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+10\sqrt{10}}{2*5}=\frac{20+10\sqrt{10}}{10}
$