5x^2-14x+1=0

Solution for 5x^2-14x+1=0 equation:

5x^2-14x+1=0

a = 5; b = -14; c = +1;
Δ = b2-4ac
Δ = -142-4·5·1
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-4\sqrt{11}}{2*5}=\frac{14-4\sqrt{11}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+4\sqrt{11}}{2*5}=\frac{14+4\sqrt{11}}{10}
$