13x^2-39x-52=0

Solution for 13x^2-39x-52=0 equation:

13x^2-39x-52=0

a = 13; b = -39; c = -52;
Δ = b2-4ac
Δ = -392-4·13·(-52)
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-65}{2*13}=\frac{-26}{26}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+65}{2*13}=\frac{104}{26}
=4
$