x+31/2x+20=65

Solution for x+31/2x+20=65 equation:

x+31/2x+20=65

We move all terms to the left:

x+31/2x+20-(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

x+31/2x-45=0

We multiply all the terms by the denominator


x*2x-45*2x+31=0

Wy multiply elements

2x^2-90x+31=0

a = 2; b = -90; c = +31;
Δ = b2-4ac
Δ = -902-4·2·31
Δ = 7852
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:

$\sqrt{\Delta}=\sqrt{7852}=\sqrt{4*1963}=\sqrt{4}*\sqrt{1963}=2\sqrt{1963}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{1963}}{2*2}=\frac{90-2\sqrt{1963}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{1963}}{2*2}=\frac{90+2\sqrt{1963}}{4}
$