31/4x=+1+2x

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

31/4x=+1+2x

We move all terms to the left:

31/4x-(+1+2x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

31/4x-(2x+1)=0

We get rid of parentheses

31/4x-2x-1=0

We multiply all the terms by the denominator


-2x*4x-1*4x+31=0

Wy multiply elements

-8x^2-4x+31=0

a = -8; b = -4; c = +31;
Δ = b2-4ac
Δ = -42-4·(-8)·31
Δ = 1008
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:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-12\sqrt{7}}{2*-8}=\frac{4-12\sqrt{7}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+12\sqrt{7}}{2*-8}=\frac{4+12\sqrt{7}}{-16}
$