30n^2=57n-18

Solution for 30n^2=57n-18 equation:

30n^2=57n-18

We move all terms to the left:

30n^2-(57n-18)=0

We get rid of parentheses

30n^2-57n+18=0

a = 30; b = -57; c = +18;
Δ = b2-4ac
Δ = -572-4·30·18
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-57)-33}{2*30}=\frac{24}{60}
=2/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+33}{2*30}=\frac{90}{60}
=1+1/2
$