2x=15-7/8x

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Solution for 2x=15-7/8x equation:



2x=15-7/8x
We move all terms to the left:
2x-(15-7/8x)=0
Domain of the equation: 8x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
2x-(-7/8x+15)=0
We get rid of parentheses
2x+7/8x-15=0
We multiply all the terms by the denominator
2x*8x-15*8x+7=0
Wy multiply elements
16x^2-120x+7=0
a = 16; b = -120; c = +7;
Δ = b2-4ac
Δ = -1202-4·16·7
Δ = 13952
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:
$\sqrt{\Delta}=\sqrt{13952}=\sqrt{64*218}=\sqrt{64}*\sqrt{218}=8\sqrt{218}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-8\sqrt{218}}{2*16}=\frac{120-8\sqrt{218}}{32} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+8\sqrt{218}}{2*16}=\frac{120+8\sqrt{218}}{32} $

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