x^2+0.8x=0.84

Solution for x^2+0.8x=0.84 equation:

x^2+0.8x=0.84

We move all terms to the left:

x^2+0.8x-(0.84)=0

We add all the numbers together, and all the variables

x^2+0.8x-0.84=0

a = 1; b = 0.8; c = -0.84;
Δ = b2-4ac
Δ = 0.82-4·1·(-0.84)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0.8)-2}{2*1}=\frac{-2.8}{2}
=-1+0.8/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.8)+2}{2*1}=\frac{1.2}{2}
=1/1.6666666666667
$