7/8x+3/4x+7/16-1/16=5/8

Solution for 7/8x+3/4x+7/16-1/16=5/8 equation:

7/8x+3/4x+7/16-1/16=5/8

We move all terms to the left:

7/8x+3/4x+7/16-1/16-(5/8)=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+7/16-1/16-(+5/8)=0

We get rid of parentheses

7/8x+3/4x+7/16-1/16-5/8=0

We calculate fractions


(-1024x^2+7)/4096x^2+448x/4096x^2+3072x/4096x^2+(-320x)/4096x^2=0

We multiply all the terms by the denominator


(-1024x^2+7)+448x+3072x+(-320x)=0

We add all the numbers together, and all the variables

(-1024x^2+7)+3520x+(-320x)=0

We get rid of parentheses

-1024x^2+3520x-320x+7=0

We add all the numbers together, and all the variables

-1024x^2+3200x+7=0

a = -1024; b = 3200; c = +7;
Δ = b2-4ac
Δ = 32002-4·(-1024)·7
Δ = 10268672
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{10268672}=\sqrt{4096*2507}=\sqrt{4096}*\sqrt{2507}=64\sqrt{2507}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3200)-64\sqrt{2507}}{2*-1024}=\frac{-3200-64\sqrt{2507}}{-2048}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3200)+64\sqrt{2507}}{2*-1024}=\frac{-3200+64\sqrt{2507}}{-2048}
$