x2+50x=10400

Solution for x2+50x=10400 equation:

x2+50x=10400

We move all terms to the left:

x2+50x-(10400)=0

We add all the numbers together, and all the variables

x^2+50x-10400=0

a = 1; b = 50; c = -10400;
Δ = b2-4ac
Δ = 502-4·1·(-10400)
Δ = 44100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{44100}=210$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-210}{2*1}=\frac{-260}{2}
=-130
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+210}{2*1}=\frac{160}{2}
=80
$