1+7/8x=9-x

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

1+7/8x=9-x

We move all terms to the left:

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


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

7/8x+1x-9+1=0

We multiply all the terms by the denominator


1x*8x-9*8x+1*8x+7=0

Wy multiply elements

8x^2-72x+8x+7=0

We add all the numbers together, and all the variables

8x^2-64x+7=0

a = 8; b = -64; c = +7;
Δ = b2-4ac
Δ = -642-4·8·7
Δ = 3872
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:

$\sqrt{\Delta}=\sqrt{3872}=\sqrt{1936*2}=\sqrt{1936}*\sqrt{2}=44\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-44\sqrt{2}}{2*8}=\frac{64-44\sqrt{2}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+44\sqrt{2}}{2*8}=\frac{64+44\sqrt{2}}{16}
$