x^2+50x+25=1000

Solution for x^2+50x+25=1000 equation:

x^2+50x+25=1000

We move all terms to the left:

x^2+50x+25-(1000)=0

We add all the numbers together, and all the variables

x^2+50x-975=0

a = 1; b = 50; c = -975;
Δ = b2-4ac
Δ = 502-4·1·(-975)
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-80}{2*1}=\frac{-130}{2}
=-65
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+80}{2*1}=\frac{30}{2}
=15
$