5n^2+14n=-8

Solution for 5n^2+14n=-8 equation:

5n^2+14n=-8

We move all terms to the left:

5n^2+14n-(-8)=0

We add all the numbers together, and all the variables

5n^2+14n+8=0

a = 5; b = 14; c = +8;
Δ = b2-4ac
Δ = 142-4·5·8
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-6}{2*5}=\frac{-20}{10}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+6}{2*5}=\frac{-8}{10}
=-4/5
$