5n^2-10n-42=-2

Solution for 5n^2-10n-42=-2 equation:

5n^2-10n-42=-2

We move all terms to the left:

5n^2-10n-42-(-2)=0

We add all the numbers together, and all the variables

5n^2-10n-40=0

a = 5; b = -10; c = -40;
Δ = b2-4ac
Δ = -102-4·5·(-40)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-30}{2*5}=\frac{-20}{10}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+30}{2*5}=\frac{40}{10}
=4
$