X^2+5x=1000

Solution for X^2+5x=1000 equation:

X^2+5X=1000

We move all terms to the left:

X^2+5X-(1000)=0

a = 1; b = 5; c = -1000;
Δ = b2-4ac
Δ = 52-4·1·(-1000)
Δ = 4025
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:

$\sqrt{\Delta}=\sqrt{4025}=\sqrt{25*161}=\sqrt{25}*\sqrt{161}=5\sqrt{161}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{161}}{2*1}=\frac{-5-5\sqrt{161}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{161}}{2*1}=\frac{-5+5\sqrt{161}}{2}
$