5n^2=6n+32

Solution for 5n^2=6n+32 equation:

5n^2=6n+32

We move all terms to the left:

5n^2-(6n+32)=0

We get rid of parentheses

5n^2-6n-32=0

a = 5; b = -6; c = -32;
Δ = b2-4ac
Δ = -62-4·5·(-32)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-26}{2*5}=\frac{-20}{10}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+26}{2*5}=\frac{32}{10}
=3+1/5
$