22x(1+x)=24

Solution for 22x(1+x)=24 equation:

22x(1+x)=24

We move all terms to the left:

22x(1+x)-(24)=0

We add all the numbers together, and all the variables

22x(x+1)-24=0

We multiply parentheses

22x^2+22x-24=0

a = 22; b = 22; c = -24;
Δ = b2-4ac
Δ = 222-4·22·(-24)
Δ = 2596
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2596}=\sqrt{4*649}=\sqrt{4}*\sqrt{649}=2\sqrt{649}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{649}}{2*22}=\frac{-22-2\sqrt{649}}{44}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{649}}{2*22}=\frac{-22+2\sqrt{649}}{44}
$