4/3x-1/4+1/16x=7/64

Solution for 4/3x-1/4+1/16x=7/64 equation:

4/3x-1/4+1/16x=7/64

We move all terms to the left:

4/3x-1/4+1/16x-(7/64)=0


Domain of the equation: 3x!=0

x!=0/3

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

4/3x+1/16x-1/4-(+7/64)=0

We get rid of parentheses

4/3x+1/16x-1/4-7/64=0

We calculate fractions


(-3072x^2)/49152x^2+(-1344x^2)/49152x^2+65536x/49152x^2+3072x/49152x^2=0

We multiply all the terms by the denominator


(-3072x^2)+(-1344x^2)+65536x+3072x=0

We add all the numbers together, and all the variables

(-3072x^2)+(-1344x^2)+68608x=0

We get rid of parentheses

-3072x^2-1344x^2+68608x=0

We add all the numbers together, and all the variables

-4416x^2+68608x=0

a = -4416; b = 68608; c = 0;
Δ = b2-4ac
Δ = 686082-4·(-4416)·0
Δ = 4707057664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4707057664}=68608$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68608)-68608}{2*-4416}=\frac{-137216}{-8832}
=15+37/69
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68608)+68608}{2*-4416}=\frac{0}{-8832}
=0
$