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

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

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

We move all terms to the left:

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


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

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

128x^2+16x-7=0

a = 128; b = 16; c = -7;
Δ = b2-4ac
Δ = 162-4·128·(-7)
Δ = 3840
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:

$\sqrt{\Delta}=\sqrt{3840}=\sqrt{256*15}=\sqrt{256}*\sqrt{15}=16\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16\sqrt{15}}{2*128}=\frac{-16-16\sqrt{15}}{256}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16\sqrt{15}}{2*128}=\frac{-16+16\sqrt{15}}{256}
$