2a^2-72a-26=0

Solution for 2a^2-72a-26=0 equation:

2a^2-72a-26=0

a = 2; b = -72; c = -26;
Δ = b2-4ac
Δ = -722-4·2·(-26)
Δ = 5392
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:

$\sqrt{\Delta}=\sqrt{5392}=\sqrt{16*337}=\sqrt{16}*\sqrt{337}=4\sqrt{337}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-4\sqrt{337}}{2*2}=\frac{72-4\sqrt{337}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+4\sqrt{337}}{2*2}=\frac{72+4\sqrt{337}}{4}
$