1/2x+16=-0.6-3x

Solution for 1/2x+16=-0.6-3x equation:

1/2x+16=-0.6-3x

We move all terms to the left:

1/2x+16-(-0.6-3x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(-3x-0.6)+16=0

We get rid of parentheses

1/2x+3x+0.6+16=0

We multiply all the terms by the denominator


3x*2x+(0.6)*2x+16*2x+1=0

We multiply parentheses

3x*2x+1.2x+16*2x+1=0

Wy multiply elements

6x^2+1.2x+32x+1=0

We add all the numbers together, and all the variables

6x^2+33.2x+1=0

a = 6; b = 33.2; c = +1;
Δ = b2-4ac
Δ = 33.22-4·6·1
Δ = 1078.24
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{-(33.2)-\sqrt{1078.24}}{2*6}=\frac{-33.2-\sqrt{1078.24}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33.2)+\sqrt{1078.24}}{2*6}=\frac{-33.2+\sqrt{1078.24}}{12}
$