x^2-9x-32x=0

Solution for x^2-9x-32x=0 equation:

x^2-9x-32x=0

We add all the numbers together, and all the variables

x^2-41x=0

a = 1; b = -41; c = 0;
Δ = b2-4ac
Δ = -412-4·1·0
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-41}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+41}{2*1}=\frac{82}{2}
=41
$