5n^2-11n=8

Solution for 5n^2-11n=8 equation:

5n^2-11n=8

We move all terms to the left:

5n^2-11n-(8)=0

a = 5; b = -11; c = -8;
Δ = b2-4ac
Δ = -112-4·5·(-8)
Δ = 281
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{281}}{2*5}=\frac{11-\sqrt{281}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{281}}{2*5}=\frac{11+\sqrt{281}}{10}
$