x+2=7/8x-14

Solution for x+2=7/8x-14 equation:

x+2=7/8x-14

We move all terms to the left:

x+2-(7/8x-14)=0


Domain of the equation: 8x-14)!=0

x∈R


We get rid of parentheses

x-7/8x+14+2=0

We multiply all the terms by the denominator


x*8x+14*8x+2*8x-7=0

Wy multiply elements

8x^2+112x+16x-7=0

We add all the numbers together, and all the variables

8x^2+128x-7=0

a = 8; b = 128; c = -7;
Δ = b2-4ac
Δ = 1282-4·8·(-7)
Δ = 16608
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:

$\sqrt{\Delta}=\sqrt{16608}=\sqrt{16*1038}=\sqrt{16}*\sqrt{1038}=4\sqrt{1038}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(128)-4\sqrt{1038}}{2*8}=\frac{-128-4\sqrt{1038}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+4\sqrt{1038}}{2*8}=\frac{-128+4\sqrt{1038}}{16}
$