x^2-28x+53=0

Solution for x^2-28x+53=0 equation:

x^2-28x+53=0

a = 1; b = -28; c = +53;
Δ = b2-4ac
Δ = -282-4·1·53
Δ = 572
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:

$\sqrt{\Delta}=\sqrt{572}=\sqrt{4*143}=\sqrt{4}*\sqrt{143}=2\sqrt{143}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{143}}{2*1}=\frac{28-2\sqrt{143}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{143}}{2*1}=\frac{28+2\sqrt{143}}{2}
$