X2+124x+49=1000

Solution for X2+124x+49=1000 equation:

X2+124X+49=1000

We move all terms to the left:

X2+124X+49-(1000)=0

We add all the numbers together, and all the variables

X^2+124X-951=0

a = 1; b = 124; c = -951;
Δ = b2-4ac
Δ = 1242-4·1·(-951)
Δ = 19180
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:

$\sqrt{\Delta}=\sqrt{19180}=\sqrt{4*4795}=\sqrt{4}*\sqrt{4795}=2\sqrt{4795}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(124)-2\sqrt{4795}}{2*1}=\frac{-124-2\sqrt{4795}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(124)+2\sqrt{4795}}{2*1}=\frac{-124+2\sqrt{4795}}{2}
$