3/8x+15/16x=1/4

Solution for 3/8x+15/16x=1/4 equation:

3/8x+15/16x=1/4

We move all terms to the left:

3/8x+15/16x-(1/4)=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+15/16x-(+1/4)=0

We get rid of parentheses

3/8x+15/16x-1/4=0

We calculate fractions


(-128x^2)/2048x^2+768x/2048x^2+1920x/2048x^2=0

We multiply all the terms by the denominator


(-128x^2)+768x+1920x=0

We add all the numbers together, and all the variables

(-128x^2)+2688x=0

We get rid of parentheses

-128x^2+2688x=0

a = -128; b = 2688; c = 0;
Δ = b2-4ac
Δ = 26882-4·(-128)·0
Δ = 7225344
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7225344}=2688$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2688)-2688}{2*-128}=\frac{-5376}{-256}
=+21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2688)+2688}{2*-128}=\frac{0}{-256}
=0
$