x^2-10x=1000

Solution for x^2-10x=1000 equation:

x^2-10x=1000

We move all terms to the left:

x^2-10x-(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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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