x^2-5x+1.25=0

Solution for x^2-5x+1.25=0 equation:

x^2-5x+1.25=0

a = 1; b = -5; c = +1.25;
Δ = b2-4ac
Δ = -52-4·1·1.25
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-2\sqrt{5}}{2*1}=\frac{5-2\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+2\sqrt{5}}{2*1}=\frac{5+2\sqrt{5}}{2}
$