(x-5)x+1=40

Solution for (x-5)x+1=40 equation:

(x-5)x+1=40

We move all terms to the left:

(x-5)x+1-(40)=0

We add all the numbers together, and all the variables

(x-5)x-39=0

We multiply parentheses

x^2-5x-39=0

a = 1; b = -5; c = -39;
Δ = b2-4ac
Δ = -52-4·1·(-39)
Δ = 181
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{-(-5)-\sqrt{181}}{2*1}=\frac{5-\sqrt{181}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{181}}{2*1}=\frac{5+\sqrt{181}}{2}
$