4x+61/2x+2=65

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Solution for 4x+61/2x+2=65 equation: 



4x+61/2x+2=65

We move all terms to the left:

4x+61/2x+2-(65)=0



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



We add all the numbers together, and all the variables

4x+61/2x-63=0

We multiply all the terms by the denominator


4x*2x-63*2x+61=0

Wy multiply elements

8x^2-126x+61=0

a = 8; b = -126; c = +61;
Δ = b2-4ac
Δ = -1262-4·8·61
Δ = 13924
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13924}=118$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-118}{2*8}=\frac{8}{16}
=1/2
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+118}{2*8}=\frac{244}{16}
=15+1/4
$

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