4x+62/4x+2=65

Solution for 4x+62/4x+2=65 equation:

4x+62/4x+2=65

We move all terms to the left:

4x+62/4x+2-(65)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

4x+62/4x-63=0

We multiply all the terms by the denominator


4x*4x-63*4x+62=0

Wy multiply elements

16x^2-252x+62=0

a = 16; b = -252; c = +62;
Δ = b2-4ac
Δ = -2522-4·16·62
Δ = 59536
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{59536}=244$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-252)-244}{2*16}=\frac{8}{32}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-252)+244}{2*16}=\frac{496}{32}
=15+1/2
$