r^2+1690r-80100=0

Solution for r^2+1690r-80100=0 equation:

r^2+1690r-80100=0

a = 1; b = 1690; c = -80100;
Δ = b2-4ac
Δ = 16902-4·1·(-80100)
Δ = 3176500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3176500}=\sqrt{100*31765}=\sqrt{100}*\sqrt{31765}=10\sqrt{31765}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1690)-10\sqrt{31765}}{2*1}=\frac{-1690-10\sqrt{31765}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1690)+10\sqrt{31765}}{2*1}=\frac{-1690+10\sqrt{31765}}{2}
$