2n2=59+12n

Solution for 2n2=59+12n equation:

2n^2=59+12n

We move all terms to the left:

2n^2-(59+12n)=0

We add all the numbers together, and all the variables

2n^2-(12n+59)=0

We get rid of parentheses

2n^2-12n-59=0

a = 2; b = -12; c = -59;
Δ = b2-4ac
Δ = -122-4·2·(-59)
Δ = 616
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{616}=\sqrt{4*154}=\sqrt{4}*\sqrt{154}=2\sqrt{154}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{154}}{2*2}=\frac{12-2\sqrt{154}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{154}}{2*2}=\frac{12+2\sqrt{154}}{4}
$