x2+2(140-x)=10000

Solution for x2+2(140-x)=10000 equation:

x2+2(140-x)=10000

We move all terms to the left:

x2+2(140-x)-(10000)=0

We add all the numbers together, and all the variables

x2+2(-1x+140)-10000=0

We add all the numbers together, and all the variables

x^2+2(-1x+140)-10000=0

We multiply parentheses

x^2-2x+280-10000=0

We add all the numbers together, and all the variables

x^2-2x-9720=0

a = 1; b = -2; c = -9720;
Δ = b2-4ac
Δ = -22-4·1·(-9720)
Δ = 38884
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:

$\sqrt{\Delta}=\sqrt{38884}=\sqrt{4*9721}=\sqrt{4}*\sqrt{9721}=2\sqrt{9721}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{9721}}{2*1}=\frac{2-2\sqrt{9721}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{9721}}{2*1}=\frac{2+2\sqrt{9721}}{2}
$