2x+3=x^2-5x-17

Solution for 2x+3=x^2-5x-17 equation:

2x+3=x^2-5x-17

We move all terms to the left:

2x+3-(x^2-5x-17)=0

We get rid of parentheses

-x^2+2x+5x+17+3=0

We add all the numbers together, and all the variables

-1x^2+7x+20=0

a = -1; b = 7; c = +20;
Δ = b2-4ac
Δ = 72-4·(-1)·20
Δ = 129
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{-(7)-\sqrt{129}}{2*-1}=\frac{-7-\sqrt{129}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{129}}{2*-1}=\frac{-7+\sqrt{129}}{-2}
$