t^2-6t-56=0

Solution for t^2-6t-56=0 equation:

t^2-6t-56=0

a = 1; b = -6; c = -56;
Δ = b2-4ac
Δ = -62-4·1·(-56)
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{65}}{2*1}=\frac{6-2\sqrt{65}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{65}}{2*1}=\frac{6+2\sqrt{65}}{2}
$