66+57n(1/2)=180

Solution for 66+57n(1/2)=180 equation:

66+57n(1/2)=180

We move all terms to the left:

66+57n(1/2)-(180)=0

We add all the numbers together, and all the variables

57n(+1/2)+66-180=0

We add all the numbers together, and all the variables

57n(+1/2)-114=0

We multiply parentheses

57n^2-114=0

a = 57; b = 0; c = -114;
Δ = b2-4ac
Δ = 02-4·57·(-114)
Δ = 25992
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:

$\sqrt{\Delta}=\sqrt{25992}=\sqrt{12996*2}=\sqrt{12996}*\sqrt{2}=114\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-114\sqrt{2}}{2*57}=\frac{0-114\sqrt{2}}{114}
=-\frac{114\sqrt{2}}{114}
=-\sqrt{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+114\sqrt{2}}{2*57}=\frac{0+114\sqrt{2}}{114}
=\frac{114\sqrt{2}}{114}
=\sqrt{2}
$