13-9x-5x^2=9

Solution for 13-9x-5x^2=9 equation:

13-9x-5x^2=9

We move all terms to the left:

13-9x-5x^2-(9)=0

We add all the numbers together, and all the variables

-5x^2-9x+4=0

a = -5; b = -9; c = +4;
Δ = b2-4ac
Δ = -92-4·(-5)·4
Δ = 161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{161}}{2*-5}=\frac{9-\sqrt{161}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{161}}{2*-5}=\frac{9+\sqrt{161}}{-10}
$