x(x+45)=-46.46

Solution for x(x+45)=-46.46 equation:

x(x+45)=-46.46

We move all terms to the left:

x(x+45)-(-46.46)=0

We add all the numbers together, and all the variables

x(x+45)+46.46=0

We multiply parentheses

x^2+45x+46.46=0

a = 1; b = 45; c = +46.46;
Δ = b2-4ac
Δ = 452-4·1·46.46
Δ = 1839.16
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{-(45)-\sqrt{1839.16}}{2*1}=\frac{-45-\sqrt{1839.16}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{1839.16}}{2*1}=\frac{-45+\sqrt{1839.16}}{2}
$