1/2x+12=-4x

Solution for 1/2x+12=-4x equation:

1/2x+12=-4x

We move all terms to the left:

1/2x+12-(-4x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x+4x+12=0

We multiply all the terms by the denominator


4x*2x+12*2x+1=0

Wy multiply elements

8x^2+24x+1=0

a = 8; b = 24; c = +1;
Δ = b2-4ac
Δ = 242-4·8·1
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{34}}{2*8}=\frac{-24-4\sqrt{34}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{34}}{2*8}=\frac{-24+4\sqrt{34}}{16}
$