1/8x+40=3x-6

Solution for 1/8x+40=3x-6 equation:

1/8x+40=3x-6

We move all terms to the left:

1/8x+40-(3x-6)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We get rid of parentheses

1/8x-3x+6+40=0

We multiply all the terms by the denominator


-3x*8x+6*8x+40*8x+1=0

Wy multiply elements

-24x^2+48x+320x+1=0

We add all the numbers together, and all the variables

-24x^2+368x+1=0

a = -24; b = 368; c = +1;
Δ = b2-4ac
Δ = 3682-4·(-24)·1
Δ = 135520
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:

$\sqrt{\Delta}=\sqrt{135520}=\sqrt{1936*70}=\sqrt{1936}*\sqrt{70}=44\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(368)-44\sqrt{70}}{2*-24}=\frac{-368-44\sqrt{70}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(368)+44\sqrt{70}}{2*-24}=\frac{-368+44\sqrt{70}}{-48}
$