23=3x2-5x+1

Solution for 23=3x2-5x+1 equation:

23=3x^2-5x+1

We move all terms to the left:

23-(3x^2-5x+1)=0

We get rid of parentheses

-3x^2+5x-1+23=0

We add all the numbers together, and all the variables

-3x^2+5x+22=0

a = -3; b = 5; c = +22;
Δ = b2-4ac
Δ = 52-4·(-3)·22
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-17}{2*-3}=\frac{-22}{-6}
=3+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+17}{2*-3}=\frac{12}{-6}
=-2
$