8-1/2x=-12x-84

Solution for 8-1/2x=-12x-84 equation:

8-1/2x=-12x-84

We move all terms to the left:

8-1/2x-(-12x-84)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

-1/2x+12x+84+8=0

We multiply all the terms by the denominator


12x*2x+84*2x+8*2x-1=0

Wy multiply elements

24x^2+168x+16x-1=0

We add all the numbers together, and all the variables

24x^2+184x-1=0

a = 24; b = 184; c = -1;
Δ = b2-4ac
Δ = 1842-4·24·(-1)
Δ = 33952
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:

$\sqrt{\Delta}=\sqrt{33952}=\sqrt{16*2122}=\sqrt{16}*\sqrt{2122}=4\sqrt{2122}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(184)-4\sqrt{2122}}{2*24}=\frac{-184-4\sqrt{2122}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(184)+4\sqrt{2122}}{2*24}=\frac{-184+4\sqrt{2122}}{48}
$