7n^2-63-10n=0

Solution for 7n^2-63-10n=0 equation:

7n^2-63-10n=0

a = 7; b = -10; c = -63;
Δ = b2-4ac
Δ = -102-4·7·(-63)
Δ = 1864
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:

$\sqrt{\Delta}=\sqrt{1864}=\sqrt{4*466}=\sqrt{4}*\sqrt{466}=2\sqrt{466}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{466}}{2*7}=\frac{10-2\sqrt{466}}{14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{466}}{2*7}=\frac{10+2\sqrt{466}}{14}
$