1/8x=7/2x-1

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Solution for 1/8x=7/2x-1 equation:



1/8x=7/2x-1
We move all terms to the left:
1/8x-(7/2x-1)=0
Domain of the equation: 8x!=0
x!=0/8
x!=0
x∈R
Domain of the equation: 2x-1)!=0
x∈R
We get rid of parentheses
1/8x-7/2x+1=0
We calculate fractions
2x/16x^2+(-56x)/16x^2+1=0
We multiply all the terms by the denominator
2x+(-56x)+1*16x^2=0
Wy multiply elements
16x^2+2x+(-56x)=0
We get rid of parentheses
16x^2+2x-56x=0
We add all the numbers together, and all the variables
16x^2-54x=0
a = 16; b = -54; c = 0;
Δ = b2-4ac
Δ = -542-4·16·0
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-54}{2*16}=\frac{0}{32} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+54}{2*16}=\frac{108}{32} =3+3/8 $

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