5t^2-6t-61=0

Solution for 5t^2-6t-61=0 equation:

5t^2-6t-61=0

a = 5; b = -6; c = -61;
Δ = b2-4ac
Δ = -62-4·5·(-61)
Δ = 1256
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:

$\sqrt{\Delta}=\sqrt{1256}=\sqrt{4*314}=\sqrt{4}*\sqrt{314}=2\sqrt{314}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{314}}{2*5}=\frac{6-2\sqrt{314}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{314}}{2*5}=\frac{6+2\sqrt{314}}{10}
$