0=3x^2-x-23

Solution for 0=3x^2-x-23 equation:

0=3x^2-x-23

We move all terms to the left:

0-(3x^2-x-23)=0

We add all the numbers together, and all the variables

-(3x^2-x-23)=0

We get rid of parentheses

-3x^2+x+23=0

a = -3; b = 1; c = +23;
Δ = b2-4ac
Δ = 12-4·(-3)·23
Δ = 277
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{277}}{2*-3}=\frac{-1-\sqrt{277}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{277}}{2*-3}=\frac{-1+\sqrt{277}}{-6}
$