7/8x+3-1/2x=9+1-1/8x

Solution for 7/8x+3-1/2x=9+1-1/8x equation:

7/8x+3-1/2x=9+1-1/8x

We move all terms to the left:

7/8x+3-1/2x-(9+1-1/8x)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

7/8x-1/2x-(-1/8x+10)+3=0

We get rid of parentheses

7/8x-1/2x+1/8x-10+3=0

We calculate fractions


(2x+7)/16x^2+(-8x)/16x^2-10+3=0

We add all the numbers together, and all the variables

(2x+7)/16x^2+(-8x)/16x^2-7=0

We multiply all the terms by the denominator


(2x+7)+(-8x)-7*16x^2=0

Wy multiply elements

-112x^2+(2x+7)+(-8x)=0

We get rid of parentheses

-112x^2+2x-8x+7=0

We add all the numbers together, and all the variables

-112x^2-6x+7=0

a = -112; b = -6; c = +7;
Δ = b2-4ac
Δ = -62-4·(-112)·7
Δ = 3172
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:

$\sqrt{\Delta}=\sqrt{3172}=\sqrt{4*793}=\sqrt{4}*\sqrt{793}=2\sqrt{793}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{793}}{2*-112}=\frac{6-2\sqrt{793}}{-224}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{793}}{2*-112}=\frac{6+2\sqrt{793}}{-224}
$