x2+4x+1.5=222

Solution for x2+4x+1.5=222 equation:

x2+4x+1.5=222

We move all terms to the left:

x2+4x+1.5-(222)=0

We add all the numbers together, and all the variables

x^2+4x-220.5=0

a = 1; b = 4; c = -220.5;
Δ = b2-4ac
Δ = 42-4·1·(-220.5)
Δ = 898
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{-(4)-\sqrt{898}}{2*1}=\frac{-4-\sqrt{898}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+\sqrt{898}}{2*1}=\frac{-4+\sqrt{898}}{2}
$