5t^2-12t-30=0

Solution for 5t^2-12t-30=0 equation:

5t^2-12t-30=0

a = 5; b = -12; c = -30;
Δ = b2-4ac
Δ = -122-4·5·(-30)
Δ = 744
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:

$\sqrt{\Delta}=\sqrt{744}=\sqrt{4*186}=\sqrt{4}*\sqrt{186}=2\sqrt{186}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{186}}{2*5}=\frac{12-2\sqrt{186}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{186}}{2*5}=\frac{12+2\sqrt{186}}{10}
$