5n^2=-11n+78

Solution for 5n^2=-11n+78 equation:

5n^2=-11n+78

We move all terms to the left:

5n^2-(-11n+78)=0

We get rid of parentheses

5n^2+11n-78=0

a = 5; b = 11; c = -78;
Δ = b2-4ac
Δ = 112-4·5·(-78)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-41}{2*5}=\frac{-52}{10}
=-5+1/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+41}{2*5}=\frac{30}{10}
=3
$