-5x^2-2x=-41

Solution for -5x^2-2x=-41 equation:

-5x^2-2x=-41

We move all terms to the left:

-5x^2-2x-(-41)=0

We add all the numbers together, and all the variables

-5x^2-2x+41=0

a = -5; b = -2; c = +41;
Δ = b2-4ac
Δ = -22-4·(-5)·41
Δ = 824
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{824}=\sqrt{4*206}=\sqrt{4}*\sqrt{206}=2\sqrt{206}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{206}}{2*-5}=\frac{2-2\sqrt{206}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{206}}{2*-5}=\frac{2+2\sqrt{206}}{-10}
$