2x^2=10x-1

Solution for 2x^2=10x-1 equation:

2x^2=10x-1

We move all terms to the left:

2x^2-(10x-1)=0

We get rid of parentheses

2x^2-10x+1=0

a = 2; b = -10; c = +1;
Δ = b2-4ac
Δ = -102-4·2·1
Δ = 92
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:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{23}}{2*2}=\frac{10-2\sqrt{23}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{23}}{2*2}=\frac{10+2\sqrt{23}}{4}
$