x-2=7/8x-15

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

x-2=7/8x-15

We move all terms to the left:

x-2-(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}
$