13x^2-4x-105=0

Solution for 13x^2-4x-105=0 equation:

13x^2-4x-105=0

a = 13; b = -4; c = -105;
Δ = b2-4ac
Δ = -42-4·13·(-105)
Δ = 5476
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5476}=74$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-74}{2*13}=\frac{-70}{26}
=-2+9/13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+74}{2*13}=\frac{78}{26}
=3
$