342=x^2+9x+20

Solution for 342=x^2+9x+20 equation:

342=x^2+9x+20

We move all terms to the left:

342-(x^2+9x+20)=0

We get rid of parentheses

-x^2-9x-20+342=0

We add all the numbers together, and all the variables

-1x^2-9x+322=0

a = -1; b = -9; c = +322;
Δ = b2-4ac
Δ = -92-4·(-1)·322
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-37}{2*-1}=\frac{-28}{-2}
=+14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+37}{2*-1}=\frac{46}{-2}
=-23
$