-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)=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-20=0

We multiply all the terms by the denominator


-2x*8x-20*8x-3=0

Wy multiply elements

-16x^2-160x-3=0

a = -16; b = -160; c = -3;
Δ = b2-4ac
Δ = -1602-4·(-16)·(-3)
Δ = 25408
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:

$\sqrt{\Delta}=\sqrt{25408}=\sqrt{64*397}=\sqrt{64}*\sqrt{397}=8\sqrt{397}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-160)-8\sqrt{397}}{2*-16}=\frac{160-8\sqrt{397}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-160)+8\sqrt{397}}{2*-16}=\frac{160+8\sqrt{397}}{-32}
$