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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2+5x+8=0

a = -1; b = 5; c = +8;
Δ = b2-4ac
Δ = 52-4·(-1)·8
Δ = 57
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{-(5)-\sqrt{57}}{2*-1}=\frac{-5-\sqrt{57}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{57}}{2*-1}=\frac{-5+\sqrt{57}}{-2}
$