X^2-55x+200=0

Solution for X^2-55x+200=0 equation:

X^2-55X+200=0

a = 1; b = -55; c = +200;
Δ = b2-4ac
Δ = -552-4·1·200
Δ = 2225
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:

$\sqrt{\Delta}=\sqrt{2225}=\sqrt{25*89}=\sqrt{25}*\sqrt{89}=5\sqrt{89}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-5\sqrt{89}}{2*1}=\frac{55-5\sqrt{89}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+5\sqrt{89}}{2*1}=\frac{55+5\sqrt{89}}{2}
$