-3/8x-20+2x=6

Solution for -3/8x-20+2x=6 equation:

-3/8x-20+2x=6

We move all terms to the left:

-3/8x-20+2x-(6)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

2x-3/8x-26=0

We multiply all the terms by the denominator


2x*8x-26*8x-3=0

Wy multiply elements

16x^2-208x-3=0

a = 16; b = -208; c = -3;
Δ = b2-4ac
Δ = -2082-4·16·(-3)
Δ = 43456
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:

$\sqrt{\Delta}=\sqrt{43456}=\sqrt{64*679}=\sqrt{64}*\sqrt{679}=8\sqrt{679}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-208)-8\sqrt{679}}{2*16}=\frac{208-8\sqrt{679}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-208)+8\sqrt{679}}{2*16}=\frac{208+8\sqrt{679}}{32}
$