X^2+6x+1=0.5

Solution for X^2+6x+1=0.5 equation:

X^2+6X+1=0.5

We move all terms to the left:

X^2+6X+1-(0.5)=0

We add all the numbers together, and all the variables

X^2+6X+0.5=0

a = 1; b = 6; c = +0.5;
Δ = b2-4ac
Δ = 62-4·1·0.5
Δ = 34
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{34}}{2*1}=\frac{-6-\sqrt{34}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+\sqrt{34}}{2*1}=\frac{-6+\sqrt{34}}{2}
$