(-x-5)x=3

Solution for (-x-5)x=3 equation:

(-x-5)x=3

We move all terms to the left:

(-x-5)x-(3)=0

We add all the numbers together, and all the variables

(-1x-5)x-3=0

We multiply parentheses

-1x^2-5x-3=0

a = -1; b = -5; c = -3;
Δ = b2-4ac
Δ = -52-4·(-1)·(-3)
Δ = 13
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{13}}{2*-1}=\frac{5-\sqrt{13}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{13}}{2*-1}=\frac{5+\sqrt{13}}{-2}
$