5n^2=-6n+63

Solution for 5n^2=-6n+63 equation:

5n^2=-6n+63

We move all terms to the left:

5n^2-(-6n+63)=0

We get rid of parentheses

5n^2+6n-63=0

a = 5; b = 6; c = -63;
Δ = b2-4ac
Δ = 62-4·5·(-63)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-36}{2*5}=\frac{-42}{10}
=-4+1/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+36}{2*5}=\frac{30}{10}
=3
$