10n^2-45-25=0

Solution for 10n^2-45-25=0 equation:

10n^2-45-25=0

We add all the numbers together, and all the variables

10n^2-70=0

a = 10; b = 0; c = -70;
Δ = b2-4ac
Δ = 02-4·10·(-70)
Δ = 2800
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:

$\sqrt{\Delta}=\sqrt{2800}=\sqrt{400*7}=\sqrt{400}*\sqrt{7}=20\sqrt{7}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{7}}{2*10}=\frac{0-20\sqrt{7}}{20}
=-\frac{20\sqrt{7}}{20}
=-\sqrt{7}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{7}}{2*10}=\frac{0+20\sqrt{7}}{20}
=\frac{20\sqrt{7}}{20}
=\sqrt{7}
$