x^2-50x+354=0

Solution for x^2-50x+354=0 equation:

x^2-50x+354=0

a = 1; b = -50; c = +354;
Δ = b2-4ac
Δ = -502-4·1·354
Δ = 1084
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:

$\sqrt{\Delta}=\sqrt{1084}=\sqrt{4*271}=\sqrt{4}*\sqrt{271}=2\sqrt{271}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{271}}{2*1}=\frac{50-2\sqrt{271}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{271}}{2*1}=\frac{50+2\sqrt{271}}{2}
$