54n^2-12n=42

Solution for 54n^2-12n=42 equation:

54n^2-12n=42

We move all terms to the left:

54n^2-12n-(42)=0

a = 54; b = -12; c = -42;
Δ = b2-4ac
Δ = -122-4·54·(-42)
Δ = 9216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9216}=96$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-96}{2*54}=\frac{-84}{108}
=-7/9
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+96}{2*54}=\frac{108}{108}
=1
$