3^2+2*3*x+x^2=0.78

Solution for 3^2+2*3*x+x^2=0.78 equation:

3^2+2*3x+x^2=0.78

We move all terms to the left:

3^2+2*3x+x^2-(0.78)=0

We add all the numbers together, and all the variables

x^2+2*3x+8.22=0

Wy multiply elements

x^2+6x+8.22=0

a = 1; b = 6; c = +8.22;
Δ = b2-4ac
Δ = 62-4·1·8.22
Δ = 3.12
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{-(6)-\sqrt{3.12}}{2*1}=\frac{-6-\sqrt{3.12}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+\sqrt{3.12}}{2*1}=\frac{-6+\sqrt{3.12}}{2}
$