x^2+65x=1000

Solution for x^2+65x=1000 equation:

x^2+65x=1000

We move all terms to the left:

x^2+65x-(1000)=0

a = 1; b = 65; c = -1000;
Δ = b2-4ac
Δ = 652-4·1·(-1000)
Δ = 8225
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:

$\sqrt{\Delta}=\sqrt{8225}=\sqrt{25*329}=\sqrt{25}*\sqrt{329}=5\sqrt{329}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(65)-5\sqrt{329}}{2*1}=\frac{-65-5\sqrt{329}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+5\sqrt{329}}{2*1}=\frac{-65+5\sqrt{329}}{2}
$