7/8x-15=x+2

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

7/8x-15=x+2

We move all terms to the left:

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


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-8x^2-16x-120x+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}
$