31/2x-16=4x

Solution for 31/2x-16=4x equation:

31/2x-16=4x

We move all terms to the left:

31/2x-16-(4x)=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+31/2x-16=0

We multiply all the terms by the denominator


-4x*2x-16*2x+31=0

Wy multiply elements

-8x^2-32x+31=0

a = -8; b = -32; c = +31;
Δ = b2-4ac
Δ = -322-4·(-8)·31
Δ = 2016
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:

$\sqrt{\Delta}=\sqrt{2016}=\sqrt{144*14}=\sqrt{144}*\sqrt{14}=12\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-12\sqrt{14}}{2*-8}=\frac{32-12\sqrt{14}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+12\sqrt{14}}{2*-8}=\frac{32+12\sqrt{14}}{-16}
$