0.2x(x+1)=22+x

Solution for 0.2x(x+1)=22+x equation:

0.2x(x+1)=22+x

We move all terms to the left:

0.2x(x+1)-(22+x)=0

We add all the numbers together, and all the variables

0.2x(x+1)-(x+22)=0

We multiply parentheses

0x^2+0x-(x+22)=0

We get rid of parentheses

0x^2+0x-x-22=0

We add all the numbers together, and all the variables

x^2-22=0

a = 1; b = 0; c = -22;
Δ = b2-4ac
Δ = 02-4·1·(-22)
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{22}}{2*1}=\frac{0-2\sqrt{22}}{2}
=-\frac{2\sqrt{22}}{2}
=-\sqrt{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{22}}{2*1}=\frac{0+2\sqrt{22}}{2}
=\frac{2\sqrt{22}}{2}
=\sqrt{22}
$