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62/4x+1+4x=65
We move all terms to the left:
62/4x+1+4x-(65)=0
Domain of the equation: 4x!=0We add all the numbers together, and all the variables
x!=0/4
x!=0
x∈R
4x+62/4x-64=0
We multiply all the terms by the denominator
4x*4x-64*4x+62=0
Wy multiply elements
16x^2-256x+62=0
a = 16; b = -256; c = +62;
Δ = b2-4ac
Δ = -2562-4·16·62
Δ = 61568
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{61568}=\sqrt{64*962}=\sqrt{64}*\sqrt{962}=8\sqrt{962}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-256)-8\sqrt{962}}{2*16}=\frac{256-8\sqrt{962}}{32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-256)+8\sqrt{962}}{2*16}=\frac{256+8\sqrt{962}}{32} $
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