3x+1=x^2-6

Solution for 3x+1=x^2-6 equation:

3x+1=x^2-6

We move all terms to the left:

3x+1-(x^2-6)=0

We get rid of parentheses

-x^2+3x+6+1=0

We add all the numbers together, and all the variables

-1x^2+3x+7=0

a = -1; b = 3; c = +7;
Δ = b2-4ac
Δ = 32-4·(-1)·7
Δ = 37
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{-(3)-\sqrt{37}}{2*-1}=\frac{-3-\sqrt{37}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{37}}{2*-1}=\frac{-3+\sqrt{37}}{-2}
$