x^2+140x-1600=0

Solution for x^2+140x-1600=0 equation:

x^2+140x-1600=0

a = 1; b = 140; c = -1600;
Δ = b2-4ac
Δ = 1402-4·1·(-1600)
Δ = 26000
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:

$\sqrt{\Delta}=\sqrt{26000}=\sqrt{400*65}=\sqrt{400}*\sqrt{65}=20\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(140)-20\sqrt{65}}{2*1}=\frac{-140-20\sqrt{65}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(140)+20\sqrt{65}}{2*1}=\frac{-140+20\sqrt{65}}{2}
$