-5n^2-8n=-10

Solution for -5n^2-8n=-10 equation:

-5n^2-8n=-10

We move all terms to the left:

-5n^2-8n-(-10)=0

We add all the numbers together, and all the variables

-5n^2-8n+10=0

a = -5; b = -8; c = +10;
Δ = b2-4ac
Δ = -82-4·(-5)·10
Δ = 264
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{66}}{2*-5}=\frac{8-2\sqrt{66}}{-10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{66}}{2*-5}=\frac{8+2\sqrt{66}}{-10}
$