2x-1=x^2+11x+19

Solution for 2x-1=x^2+11x+19 equation:

2x-1=x^2+11x+19

We move all terms to the left:

2x-1-(x^2+11x+19)=0

We get rid of parentheses

-x^2+2x-11x-19-1=0

We add all the numbers together, and all the variables

-1x^2-9x-20=0

a = -1; b = -9; c = -20;
Δ = b2-4ac
Δ = -92-4·(-1)·(-20)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-1}{2*-1}=\frac{8}{-2}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+1}{2*-1}=\frac{10}{-2}
=-5
$