x^2+9x-5=65

Solution for x^2+9x-5=65 equation:

x^2+9x-5=65

We move all terms to the left:

x^2+9x-5-(65)=0

We add all the numbers together, and all the variables

x^2+9x-70=0

a = 1; b = 9; c = -70;
Δ = b2-4ac
Δ = 92-4·1·(-70)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-19}{2*1}=\frac{-28}{2}
=-14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+19}{2*1}=\frac{10}{2}
=5
$