7/8x-1/4+3/4x=1/16=x

Solution for 7/8x-1/4+3/4x=1/16=x equation:

7/8x-1/4+3/4x=1/16=x

We move all terms to the left:

7/8x-1/4+3/4x-(1/16)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

7/8x+3/4x-1/4-(+1/16)=0

We get rid of parentheses

7/8x+3/4x-1/4-1/16=0

We calculate fractions


(-512x^2)/8192x^2+7168x/8192x^2+384x/8192x^2+(-128x)/8192x^2=0

We multiply all the terms by the denominator


(-512x^2)+7168x+384x+(-128x)=0

We add all the numbers together, and all the variables

(-512x^2)+7552x+(-128x)=0

We get rid of parentheses

-512x^2+7552x-128x=0

We add all the numbers together, and all the variables

-512x^2+7424x=0

a = -512; b = 7424; c = 0;
Δ = b2-4ac
Δ = 74242-4·(-512)·0
Δ = 55115776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{55115776}=7424$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7424)-7424}{2*-512}=\frac{-14848}{-1024}
=14+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7424)+7424}{2*-512}=\frac{0}{-1024}
=0
$