x^2+0.9x=2.2

Solution for x^2+0.9x=2.2 equation:

x^2+0.9x=2.2

We move all terms to the left:

x^2+0.9x-(2.2)=0

We add all the numbers together, and all the variables

x^2+0.9x-2.2=0

a = 1; b = 0.9; c = -2.2;
Δ = b2-4ac
Δ = 0.92-4·1·(-2.2)
Δ = 9.61
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{-(0.9)-\sqrt{9.61}}{2*1}=\frac{-0.9-\sqrt{9.61}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.9)+\sqrt{9.61}}{2*1}=\frac{-0.9+\sqrt{9.61}}{2}
$