5x^2-10+1=0

Solution for 5x^2-10+1=0 equation:

5x^2-10+1=0

We add all the numbers together, and all the variables

5x^2-9=0

a = 5; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·5·(-9)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{5}}{2*5}=\frac{0-6\sqrt{5}}{10}
=-\frac{6\sqrt{5}}{10}
=-\frac{3\sqrt{5}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{5}}{2*5}=\frac{0+6\sqrt{5}}{10}
=\frac{6\sqrt{5}}{10}
=\frac{3\sqrt{5}}{5}
$