X-16=4/2x+12-1x-28

Solution for X-16=4/2x+12-1x-28 equation:

X-16=4/2X+12-1X-28

We move all terms to the left:

X-16-(4/2X+12-1X-28)=0


Domain of the equation: 2X+12-1X-28)!=0

We move all terms containing X to the left, all other terms to the right

2X-1X-28)!=-12

X∈R


We add all the numbers together, and all the variables

X-(-1X+4/2X-16)-16=0

We get rid of parentheses

X+1X-4/2X+16-16=0

We multiply all the terms by the denominator


X*2X+1X*2X+16*2X-16*2X-4=0

Wy multiply elements

2X^2+2X^2+32X-32X-4=0

We add all the numbers together, and all the variables

4X^2-4=0

a = 4; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·4·(-4)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8}{2*4}=\frac{-8}{8}
=-1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8}{2*4}=\frac{8}{8}
=1
$