2n2-5n=42

Solution for 2n2-5n=42 equation:

2n^2-5n=42

We move all terms to the left:

2n^2-5n-(42)=0

a = 2; b = -5; c = -42;
Δ = b2-4ac
Δ = -52-4·2·(-42)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-19}{2*2}=\frac{-14}{4}
=-3+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+19}{2*2}=\frac{24}{4}
=6
$