7/8x-x=18

Solution for 7/8x-x=18 equation:

7/8x-x=18

We move all terms to the left:

7/8x-x-(18)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+7/8x-18=0

We multiply all the terms by the denominator


-1x*8x-18*8x+7=0

Wy multiply elements

-8x^2-144x+7=0

a = -8; b = -144; c = +7;
Δ = b2-4ac
Δ = -1442-4·(-8)·7
Δ = 20960
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:

$\sqrt{\Delta}=\sqrt{20960}=\sqrt{16*1310}=\sqrt{16}*\sqrt{1310}=4\sqrt{1310}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-4\sqrt{1310}}{2*-8}=\frac{144-4\sqrt{1310}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+4\sqrt{1310}}{2*-8}=\frac{144+4\sqrt{1310}}{-16}
$