2n^2+35n=123

Solution for 2n^2+35n=123 equation:

2n^2+35n=123

We move all terms to the left:

2n^2+35n-(123)=0

a = 2; b = 35; c = -123;
Δ = b2-4ac
Δ = 352-4·2·(-123)
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-47}{2*2}=\frac{-82}{4}
=-20+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+47}{2*2}=\frac{12}{4}
=3
$