2+x=7/8x+15

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

2+x=7/8x+15

We move all terms to the left:

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


Domain of the equation: 8x+15)!=0

x∈R


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 = 11040
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:

$\sqrt{\Delta}=\sqrt{11040}=\sqrt{16*690}=\sqrt{16}*\sqrt{690}=4\sqrt{690}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-104)-4\sqrt{690}}{2*8}=\frac{104-4\sqrt{690}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-104)+4\sqrt{690}}{2*8}=\frac{104+4\sqrt{690}}{16}
$