X2-140x-10500=0

Solution for X2-140x-10500=0 equation:

X2-140X-10500=0

We add all the numbers together, and all the variables

X^2-140X-10500=0

a = 1; b = -140; c = -10500;
Δ = b2-4ac
Δ = -1402-4·1·(-10500)
Δ = 61600
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:

$\sqrt{\Delta}=\sqrt{61600}=\sqrt{400*154}=\sqrt{400}*\sqrt{154}=20\sqrt{154}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-20\sqrt{154}}{2*1}=\frac{140-20\sqrt{154}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+20\sqrt{154}}{2*1}=\frac{140+20\sqrt{154}}{2}
$