-x+2=x^2+5x+7

Solution for -x+2=x^2+5x+7 equation:

-x+2=x^2+5x+7

We move all terms to the left:

-x+2-(x^2+5x+7)=0

We add all the numbers together, and all the variables

-1x-(x^2+5x+7)+2=0

We get rid of parentheses

-x^2-1x-5x-7+2=0

We add all the numbers together, and all the variables

-1x^2-6x-5=0

a = -1; b = -6; c = -5;
Δ = b2-4ac
Δ = -62-4·(-1)·(-5)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4}{2*-1}=\frac{2}{-2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4}{2*-1}=\frac{10}{-2}
=-5
$