13x^2-28x+1=0

Solution for 13x^2-28x+1=0 equation:

13x^2-28x+1=0

a = 13; b = -28; c = +1;
Δ = b2-4ac
Δ = -282-4·13·1
Δ = 732
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:

$\sqrt{\Delta}=\sqrt{732}=\sqrt{4*183}=\sqrt{4}*\sqrt{183}=2\sqrt{183}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{183}}{2*13}=\frac{28-2\sqrt{183}}{26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{183}}{2*13}=\frac{28+2\sqrt{183}}{26}
$