.5x+3=1/8x-12

Solution for .5x+3=1/8x-12 equation:

.5x+3=1/8x-12

We move all terms to the left:

.5x+3-(1/8x-12)=0


Domain of the equation: 8x-12)!=0

x∈R


We get rid of parentheses

.5x-1/8x+12+3=0

We multiply all the terms by the denominator


(.5x)*8x+12*8x+3*8x-1=0

We add all the numbers together, and all the variables

(+.5x)*8x+12*8x+3*8x-1=0

We multiply parentheses

8x^2+12*8x+3*8x-1=0

Wy multiply elements

8x^2+96x+24x-1=0

We add all the numbers together, and all the variables

8x^2+120x-1=0

a = 8; b = 120; c = -1;
Δ = b2-4ac
Δ = 1202-4·8·(-1)
Δ = 14432
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:

$\sqrt{\Delta}=\sqrt{14432}=\sqrt{16*902}=\sqrt{16}*\sqrt{902}=4\sqrt{902}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-4\sqrt{902}}{2*8}=\frac{-120-4\sqrt{902}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+4\sqrt{902}}{2*8}=\frac{-120+4\sqrt{902}}{16}
$