0.9x(x+200)=0.8x+22

Solution for 0.9x(x+200)=0.8x+22 equation:

0.9x(x+200)=0.8x+22

We move all terms to the left:

0.9x(x+200)-(0.8x+22)=0

We multiply parentheses

0x^2+0x-(0.8x+22)=0

We get rid of parentheses

0x^2+0x-0.8x-22=0

We add all the numbers together, and all the variables

x^2+0.2x-22=0

a = 1; b = 0.2; c = -22;
Δ = b2-4ac
Δ = 0.22-4·1·(-22)
Δ = 88.04
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{-(0.2)-\sqrt{88.04}}{2*1}=\frac{-0.2-\sqrt{88.04}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.2)+\sqrt{88.04}}{2*1}=\frac{-0.2+\sqrt{88.04}}{2}
$