8(1/4x-3)=8(3/8x)

Solution for 8(1/4x-3)=8(3/8x) equation:

8(1/4x-3)=8(3/8x)

We move all terms to the left:

8(1/4x-3)-(8(3/8x))=0


Domain of the equation: 4x-3)!=0

x∈R



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

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

8(1/4x-3)-(8(+3/8x))=0

We multiply parentheses

8x-(8(+3/8x))-24=0

We multiply all the terms by the denominator


8x*8x))-(8(-24*8x))+3=0

Wy multiply elements

64x^2-192x=0

a = 64; b = -192; c = 0;
Δ = b2-4ac
Δ = -1922-4·64·0
Δ = 36864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36864}=192$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-192)-192}{2*64}=\frac{0}{128}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-192)+192}{2*64}=\frac{384}{128}
=3
$