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^2-136x-7=0

a = 8; b = -136; c = -7;
Δ = b2-4ac
Δ = -1362-4·8·(-7)
Δ = 18720
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:

$\sqrt{\Delta}=\sqrt{18720}=\sqrt{144*130}=\sqrt{144}*\sqrt{130}=12\sqrt{130}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-136)-12\sqrt{130}}{2*8}=\frac{136-12\sqrt{130}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-136)+12\sqrt{130}}{2*8}=\frac{136+12\sqrt{130}}{16}
$