25n^2-11=12

Solution for 25n^2-11=12 equation:

25n^2-11=12

We move all terms to the left:

25n^2-11-(12)=0

We add all the numbers together, and all the variables

25n^2-23=0

a = 25; b = 0; c = -23;
Δ = b2-4ac
Δ = 02-4·25·(-23)
Δ = 2300
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:

$\sqrt{\Delta}=\sqrt{2300}=\sqrt{100*23}=\sqrt{100}*\sqrt{23}=10\sqrt{23}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{23}}{2*25}=\frac{0-10\sqrt{23}}{50}
=-\frac{10\sqrt{23}}{50}
=-\frac{\sqrt{23}}{5}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{23}}{2*25}=\frac{0+10\sqrt{23}}{50}
=\frac{10\sqrt{23}}{50}
=\frac{\sqrt{23}}{5}
$