(1/2)(x)+3=-22x

Solution for (1/2)(x)+3=-22x equation:

(1/2)(x)+3=-22x

We move all terms to the left:

(1/2)(x)+3-(-22x)=0


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/2)x-(-22x)+3=0

We multiply parentheses

x^2-(-22x)+3=0

We get rid of parentheses

x^2+22x+3=0

a = 1; b = 22; c = +3;
Δ = b2-4ac
Δ = 222-4·1·3
Δ = 472
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{472}=\sqrt{4*118}=\sqrt{4}*\sqrt{118}=2\sqrt{118}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{118}}{2*1}=\frac{-22-2\sqrt{118}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{118}}{2*1}=\frac{-22+2\sqrt{118}}{2}
$