2x+10=x^2-4x-17

Solution for 2x+10=x^2-4x-17 equation:

2x+10=x^2-4x-17

We move all terms to the left:

2x+10-(x^2-4x-17)=0

We get rid of parentheses

-x^2+2x+4x+17+10=0

We add all the numbers together, and all the variables

-1x^2+6x+27=0

a = -1; b = 6; c = +27;
Δ = b2-4ac
Δ = 62-4·(-1)·27
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-12}{2*-1}=\frac{-18}{-2}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+12}{2*-1}=\frac{6}{-2}
=-3
$