X+19=x2-11

Solution for X+19=x2-11 equation:

X+19=X2-11

We move all terms to the left:

X+19-(X2-11)=0

We add all the numbers together, and all the variables

-(+X^2-11)+X+19=0

We get rid of parentheses

-X^2+X+11+19=0

We add all the numbers together, and all the variables

-1X^2+X+30=0

a = -1; b = 1; c = +30;
Δ = b2-4ac
Δ = 12-4·(-1)·30
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-11}{2*-1}=\frac{-12}{-2}
=+6
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+11}{2*-1}=\frac{10}{-2}
=-5
$