x^2+10x=880^2

Solution for x^2+10x=880^2 equation:

x^2+10x=880^2

We move all terms to the left:

x^2+10x-(880^2)=0

We add all the numbers together, and all the variables

x^2+10x-774400=0

a = 1; b = 10; c = -774400;
Δ = b2-4ac
Δ = 102-4·1·(-774400)
Δ = 3097700
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:

$\sqrt{\Delta}=\sqrt{3097700}=\sqrt{100*30977}=\sqrt{100}*\sqrt{30977}=10\sqrt{30977}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{30977}}{2*1}=\frac{-10-10\sqrt{30977}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{30977}}{2*1}=\frac{-10+10\sqrt{30977}}{2}
$