3/8x+16=4x

Solution for 3/8x+16=4x equation:

3/8x+16=4x

We move all terms to the left:

3/8x+16-(4x)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

-4x+3/8x+16=0

We multiply all the terms by the denominator


-4x*8x+16*8x+3=0

Wy multiply elements

-32x^2+128x+3=0

a = -32; b = 128; c = +3;
Δ = b2-4ac
Δ = 1282-4·(-32)·3
Δ = 16768
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:

$\sqrt{\Delta}=\sqrt{16768}=\sqrt{64*262}=\sqrt{64}*\sqrt{262}=8\sqrt{262}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(128)-8\sqrt{262}}{2*-32}=\frac{-128-8\sqrt{262}}{-64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+8\sqrt{262}}{2*-32}=\frac{-128+8\sqrt{262}}{-64}
$