26x^2-28x-52=0

Solution for 26x^2-28x-52=0 equation:

26x^2-28x-52=0

a = 26; b = -28; c = -52;
Δ = b2-4ac
Δ = -282-4·26·(-52)
Δ = 6192
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6192}=\sqrt{144*43}=\sqrt{144}*\sqrt{43}=12\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-12\sqrt{43}}{2*26}=\frac{28-12\sqrt{43}}{52}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+12\sqrt{43}}{2*26}=\frac{28+12\sqrt{43}}{52}
$