13a^2-26a-55=0

Solution for 13a^2-26a-55=0 equation:

13a^2-26a-55=0

a = 13; b = -26; c = -55;
Δ = b2-4ac
Δ = -262-4·13·(-55)
Δ = 3536
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3536}=\sqrt{16*221}=\sqrt{16}*\sqrt{221}=4\sqrt{221}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-4\sqrt{221}}{2*13}=\frac{26-4\sqrt{221}}{26}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+4\sqrt{221}}{2*13}=\frac{26+4\sqrt{221}}{26}
$