1.5n^2-32.5=5

Solution for 1.5n^2-32.5=5 equation:

1.5n^2-32.5=5

We move all terms to the left:

1.5n^2-32.5-(5)=0

We add all the numbers together, and all the variables

1.5n^2-37.5=0

a = 1.5; b = 0; c = -37.5;
Δ = b2-4ac
Δ = 02-4·1.5·(-37.5)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-15}{2*1.5}=\frac{-15}{3}
=-5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+15}{2*1.5}=\frac{15}{3}
=5
$