t^2-26t-9=0

Solution for t^2-26t-9=0 equation:

t^2-26t-9=0

a = 1; b = -26; c = -9;
Δ = b2-4ac
Δ = -262-4·1·(-9)
Δ = 712
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:

$\sqrt{\Delta}=\sqrt{712}=\sqrt{4*178}=\sqrt{4}*\sqrt{178}=2\sqrt{178}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{178}}{2*1}=\frac{26-2\sqrt{178}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{178}}{2*1}=\frac{26+2\sqrt{178}}{2}
$