9x+19=x*x

Solution for 9x+19=x*x equation:

9x+19=x*x

We move all terms to the left:

9x+19-(x*x)=0

We add all the numbers together, and all the variables

9x-(+x*x)+19=0

We get rid of parentheses

9x-x*x+19=0

Wy multiply elements

-1x^2+9x+19=0

a = -1; b = 9; c = +19;
Δ = b2-4ac
Δ = 92-4·(-1)·19
Δ = 157
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{-(9)-\sqrt{157}}{2*-1}=\frac{-9-\sqrt{157}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{157}}{2*-1}=\frac{-9+\sqrt{157}}{-2}
$