5x^2-x+1=3

Solution for 5x^2-x+1=3 equation:

5x^2-x+1=3

We move all terms to the left:

5x^2-x+1-(3)=0

We add all the numbers together, and all the variables

5x^2-1x-2=0

a = 5; b = -1; c = -2;
Δ = b2-4ac
Δ = -12-4·5·(-2)
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{41}}{2*5}=\frac{1-\sqrt{41}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{41}}{2*5}=\frac{1+\sqrt{41}}{10}
$