3/8x+4+3/16x=2

Solution for 3/8x+4+3/16x=2 equation:

3/8x+4+3/16x=2

We move all terms to the left:

3/8x+4+3/16x-(2)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 16x!=0

x!=0/16

x!=0

x∈R


We add all the numbers together, and all the variables

3/8x+3/16x+2=0

We calculate fractions


48x/128x^2+24x/128x^2+2=0

We multiply all the terms by the denominator


48x+24x+2*128x^2=0

We add all the numbers together, and all the variables

72x+2*128x^2=0

Wy multiply elements

256x^2+72x=0

a = 256; b = 72; c = 0;
Δ = b2-4ac
Δ = 722-4·256·0
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-72}{2*256}=\frac{-144}{512}
=-9/32
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+72}{2*256}=\frac{0}{512}
=0
$