x+1=3x^2-13

Solution for x+1=3x^2-13 equation:

x+1=3x^2-13

We move all terms to the left:

x+1-(3x^2-13)=0

We get rid of parentheses

-3x^2+x+13+1=0

We add all the numbers together, and all the variables

-3x^2+x+14=0

a = -3; b = 1; c = +14;
Δ = b2-4ac
Δ = 12-4·(-3)·14
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-13}{2*-3}=\frac{-14}{-6}
=2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+13}{2*-3}=\frac{12}{-6}
=-2
$