8x-9=7/2x

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Solution for 8x-9=7/2x equation:



8x-9=7/2x
We move all terms to the left:
8x-9-(7/2x)=0
Domain of the equation: 2x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
8x-(+7/2x)-9=0
We get rid of parentheses
8x-7/2x-9=0
We multiply all the terms by the denominator
8x*2x-9*2x-7=0
Wy multiply elements
16x^2-18x-7=0
a = 16; b = -18; c = -7;
Δ = b2-4ac
Δ = -182-4·16·(-7)
Δ = 772
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:
$\sqrt{\Delta}=\sqrt{772}=\sqrt{4*193}=\sqrt{4}*\sqrt{193}=2\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{193}}{2*16}=\frac{18-2\sqrt{193}}{32} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{193}}{2*16}=\frac{18+2\sqrt{193}}{32} $

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