31/4x+1(2x)=65

Solution for 31/4x+1(2x)=65 equation:

31/4x+1(2x)=65

We move all terms to the left:

31/4x+1(2x)-(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

12x+31/4x-65=0

We multiply all the terms by the denominator


12x*4x-65*4x+31=0

Wy multiply elements

48x^2-260x+31=0

a = 48; b = -260; c = +31;
Δ = b2-4ac
Δ = -2602-4·48·31
Δ = 61648
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:

$\sqrt{\Delta}=\sqrt{61648}=\sqrt{16*3853}=\sqrt{16}*\sqrt{3853}=4\sqrt{3853}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-260)-4\sqrt{3853}}{2*48}=\frac{260-4\sqrt{3853}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-260)+4\sqrt{3853}}{2*48}=\frac{260+4\sqrt{3853}}{96}
$