7x+5/8x-3=4

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Solution for 7x+5/8x-3=4 equation:



7x+5/8x-3=4
We move all terms to the left:
7x+5/8x-3-(4)=0
Domain of the equation: 8x!=0
x!=0/8
x!=0
x∈R
We add all the numbers together, and all the variables
7x+5/8x-7=0
We multiply all the terms by the denominator
7x*8x-7*8x+5=0
Wy multiply elements
56x^2-56x+5=0
a = 56; b = -56; c = +5;
Δ = b2-4ac
Δ = -562-4·56·5
Δ = 2016
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:
$\sqrt{\Delta}=\sqrt{2016}=\sqrt{144*14}=\sqrt{144}*\sqrt{14}=12\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-12\sqrt{14}}{2*56}=\frac{56-12\sqrt{14}}{112} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+12\sqrt{14}}{2*56}=\frac{56+12\sqrt{14}}{112} $

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