u^2+10u-1000=0

Solution for u^2+10u-1000=0 equation:

u^2+10u-1000=0

a = 1; b = 10; c = -1000;
Δ = b2-4ac
Δ = 102-4·1·(-1000)
Δ = 4100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4100}=\sqrt{100*41}=\sqrt{100}*\sqrt{41}=10\sqrt{41}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{41}}{2*1}=\frac{-10-10\sqrt{41}}{2}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{41}}{2*1}=\frac{-10+10\sqrt{41}}{2}
$