X^2+100x+80=616000

Solution for X^2+100x+80=616000 equation:

X^2+100X+80=616000

We move all terms to the left:

X^2+100X+80-(616000)=0

We add all the numbers together, and all the variables

X^2+100X-615920=0

a = 1; b = 100; c = -615920;
Δ = b2-4ac
Δ = 1002-4·1·(-615920)
Δ = 2473680
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:

$\sqrt{\Delta}=\sqrt{2473680}=\sqrt{16*154605}=\sqrt{16}*\sqrt{154605}=4\sqrt{154605}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-4\sqrt{154605}}{2*1}=\frac{-100-4\sqrt{154605}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+4\sqrt{154605}}{2*1}=\frac{-100+4\sqrt{154605}}{2}
$