n^2+7n-10^6=0

Solution for n^2+7n-10^6=0 equation:

n^2+7n-10^6=0

We add all the numbers together, and all the variables

n^2+7n-1000000=0

a = 1; b = 7; c = -1000000;
Δ = b2-4ac
Δ = 72-4·1·(-1000000)
Δ = 4000049
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:

$\sqrt{\Delta}=\sqrt{4000049}=\sqrt{289*13841}=\sqrt{289}*\sqrt{13841}=17\sqrt{13841}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-17\sqrt{13841}}{2*1}=\frac{-7-17\sqrt{13841}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+17\sqrt{13841}}{2*1}=\frac{-7+17\sqrt{13841}}{2}
$