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

Solution for 3x+1=x^2+7x-1 equation:

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2-4x+2=0

a = -1; b = -4; c = +2;
Δ = b2-4ac
Δ = -42-4·(-1)·2
Δ = 24
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{6}}{2*-1}=\frac{4-2\sqrt{6}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{6}}{2*-1}=\frac{4+2\sqrt{6}}{-2}
$