X^2-55x+300=0

Solution for X^2-55x+300=0 equation:

X^2-55X+300=0

a = 1; b = -55; c = +300;
Δ = b2-4ac
Δ = -552-4·1·300
Δ = 1825
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:

$\sqrt{\Delta}=\sqrt{1825}=\sqrt{25*73}=\sqrt{25}*\sqrt{73}=5\sqrt{73}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-5\sqrt{73}}{2*1}=\frac{55-5\sqrt{73}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+5\sqrt{73}}{2*1}=\frac{55+5\sqrt{73}}{2}
$