13x*x-41x-120=0

Solution for 13x*x-41x-120=0 equation:

13x*x-41x-120=0

We add all the numbers together, and all the variables

-41x+13x*x-120=0

Wy multiply elements

13x^2-41x-120=0

a = 13; b = -41; c = -120;
Δ = b2-4ac
Δ = -412-4·13·(-120)
Δ = 7921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7921}=89$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-89}{2*13}=\frac{-48}{26}
=-1+11/13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+89}{2*13}=\frac{130}{26}
=5
$