10n+7=25n^2

Solution for 10n+7=25n^2 equation:

10n+7=25n^2

We move all terms to the left:

10n+7-(25n^2)=0

determiningTheFunctionDomain
-25n^2+10n+7=0

a = -25; b = 10; c = +7;
Δ = b2-4ac
Δ = 102-4·(-25)·7
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-20\sqrt{2}}{2*-25}=\frac{-10-20\sqrt{2}}{-50}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+20\sqrt{2}}{2*-25}=\frac{-10+20\sqrt{2}}{-50}
$