(1+x)x=0.24

Solution for (1+x)x=0.24 equation:

(1+x)x=0.24

We move all terms to the left:

(1+x)x-(0.24)=0

We add all the numbers together, and all the variables

(x+1)x-(0.24)=0

We add all the numbers together, and all the variables

(x+1)x-0.24=0

We multiply parentheses

x^2+x-0.24=0

a = 1; b = 1; c = -0.24;
Δ = b2-4ac
Δ = 12-4·1·(-0.24)
Δ = 1.96
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{-(1)-\sqrt{1.96}}{2*1}=\frac{-1-\sqrt{1.96}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1.96}}{2*1}=\frac{-1+\sqrt{1.96}}{2}
$