x^2-56x+175=0

Solution for x^2-56x+175=0 equation:

x^2-56x+175=0

a = 1; b = -56; c = +175;
Δ = b2-4ac
Δ = -562-4·1·175
Δ = 2436
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:

$\sqrt{\Delta}=\sqrt{2436}=\sqrt{4*609}=\sqrt{4}*\sqrt{609}=2\sqrt{609}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-2\sqrt{609}}{2*1}=\frac{56-2\sqrt{609}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+2\sqrt{609}}{2*1}=\frac{56+2\sqrt{609}}{2}
$