2x+1=(x+4)+3/8x

Solution for 2x+1=(x+4)+3/8x equation:

2x+1=(x+4)+3/8x

We move all terms to the left:

2x+1-((x+4)+3/8x)=0


Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


2x*8x)-((x+4)+1*8x)+3=0

Wy multiply elements

16x^2+8x=0

a = 16; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·16·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*16}=\frac{-16}{32}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*16}=\frac{0}{32}
=0
$