x(24,663+x)=40,145

Solution for x(24,663+x)=40,145 equation:

x(24.663+x)=40.145

We move all terms to the left:

x(24.663+x)-(40.145)=0

We add all the numbers together, and all the variables

x(x+24.663)-(40.145)=0

We add all the numbers together, and all the variables

x(x+24.663)-40.145=0

We multiply parentheses

x^2+24.663x-40.145=0

a = 1; b = 24.663; c = -40.145;
Δ = b2-4ac
Δ = 24.6632-4·1·(-40.145)
Δ = 768.843569
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{-(24.663)-\sqrt{768.843569}}{2*1}=\frac{-24.663-\sqrt{768.843569}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24.663)+\sqrt{768.843569}}{2*1}=\frac{-24.663+\sqrt{768.843569}}{2}
$