9,645=x^2+40x+45

Solution for 9,645=x^2+40x+45 equation:

9.645=x^2+40x+45

We move all terms to the left:

9.645-(x^2+40x+45)=0

We get rid of parentheses

-x^2-40x-45+9.645=0

We add all the numbers together, and all the variables

-1x^2-40x-35.355=0

a = -1; b = -40; c = -35.355;
Δ = b2-4ac
Δ = -402-4·(-1)·(-35.355)
Δ = 1458.58
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{-(-40)-\sqrt{1458.58}}{2*-1}=\frac{40-\sqrt{1458.58}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+\sqrt{1458.58}}{2*-1}=\frac{40+\sqrt{1458.58}}{-2}
$