2+x=15-7/8x

Solution for 2+x=15-7/8x equation:

2+x=15-7/8x

We move all terms to the left:

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


Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(-7/8x+15)+2=0

We get rid of parentheses

x+7/8x-15+2=0

We multiply all the terms by the denominator


x*8x-15*8x+2*8x+7=0

Wy multiply elements

8x^2-120x+16x+7=0

We add all the numbers together, and all the variables

8x^2-104x+7=0

a = 8; b = -104; c = +7;
Δ = b2-4ac
Δ = -1042-4·8·7
Δ = 10592
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:

$\sqrt{\Delta}=\sqrt{10592}=\sqrt{16*662}=\sqrt{16}*\sqrt{662}=4\sqrt{662}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-104)-4\sqrt{662}}{2*8}=\frac{104-4\sqrt{662}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-104)+4\sqrt{662}}{2*8}=\frac{104+4\sqrt{662}}{16}
$