X^2-685x-4500=0

Solution for X^2-685x-4500=0 equation:

X^2-685X-4500=0

a = 1; b = -685; c = -4500;
Δ = b2-4ac
Δ = -6852-4·1·(-4500)
Δ = 487225
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:

$\sqrt{\Delta}=\sqrt{487225}=\sqrt{25*19489}=\sqrt{25}*\sqrt{19489}=5\sqrt{19489}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-685)-5\sqrt{19489}}{2*1}=\frac{685-5\sqrt{19489}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-685)+5\sqrt{19489}}{2*1}=\frac{685+5\sqrt{19489}}{2}
$