7x^2-10x+1=0

Solution for 7x^2-10x+1=0 equation:

7x^2-10x+1=0

a = 7; b = -10; c = +1;
Δ = b2-4ac
Δ = -102-4·7·1
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6\sqrt{2}}{2*7}=\frac{10-6\sqrt{2}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6\sqrt{2}}{2*7}=\frac{10+6\sqrt{2}}{14}
$