7-9/8x=15+x

Solution for 7-9/8x=15+x equation:

7-9/8x=15+x

We move all terms to the left:

7-9/8x-(15+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

-9/8x-(x+15)+7=0

We get rid of parentheses

-9/8x-x-15+7=0

We multiply all the terms by the denominator


-x*8x-15*8x+7*8x-9=0

Wy multiply elements

-8x^2-120x+56x-9=0

We add all the numbers together, and all the variables

-8x^2-64x-9=0

a = -8; b = -64; c = -9;
Δ = b2-4ac
Δ = -642-4·(-8)·(-9)
Δ = 3808
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:

$\sqrt{\Delta}=\sqrt{3808}=\sqrt{16*238}=\sqrt{16}*\sqrt{238}=4\sqrt{238}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-4\sqrt{238}}{2*-8}=\frac{64-4\sqrt{238}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+4\sqrt{238}}{2*-8}=\frac{64+4\sqrt{238}}{-16}
$