-40=-2(-8+5n)2n

Solution for -40=-2(-8+5n)2n equation:

-40=-2(-8+5n)2n

We move all terms to the left:

-40-(-2(-8+5n)2n)=0

We add all the numbers together, and all the variables

-(-2(5n-8)2n)-40=0


We calculate terms in parentheses: -(-2(5n-8)2n), so:

-2(5n-8)2n

We multiply parentheses

-20n^2+32n

Back to the equation:

-(-20n^2+32n)


We get rid of parentheses

20n^2-32n-40=0

a = 20; b = -32; c = -40;
Δ = b2-4ac
Δ = -322-4·20·(-40)
Δ = 4224
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:

$\sqrt{\Delta}=\sqrt{4224}=\sqrt{64*66}=\sqrt{64}*\sqrt{66}=8\sqrt{66}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8\sqrt{66}}{2*20}=\frac{32-8\sqrt{66}}{40}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8\sqrt{66}}{2*20}=\frac{32+8\sqrt{66}}{40}
$