13n^2-245=8n^2

Solution for 13n^2-245=8n^2 equation:

13n^2-245=8n^2

We move all terms to the left:

13n^2-245-(8n^2)=0

We add all the numbers together, and all the variables

5n^2-245=0

a = 5; b = 0; c = -245;
Δ = b2-4ac
Δ = 02-4·5·(-245)
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-70}{2*5}=\frac{-70}{10}
=-7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+70}{2*5}=\frac{70}{10}
=7
$