-1/8x=x-7

Solution for -1/8x=x-7 equation:

-1/8x=x-7

We move all terms to the left:

-1/8x-(x-7)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We get rid of parentheses

-1/8x-x+7=0

We multiply all the terms by the denominator


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

Wy multiply elements

-8x^2+56x-1=0

a = -8; b = 56; c = -1;
Δ = b2-4ac
Δ = 562-4·(-8)·(-1)
Δ = 3104
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:

$\sqrt{\Delta}=\sqrt{3104}=\sqrt{16*194}=\sqrt{16}*\sqrt{194}=4\sqrt{194}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-4\sqrt{194}}{2*-8}=\frac{-56-4\sqrt{194}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+4\sqrt{194}}{2*-8}=\frac{-56+4\sqrt{194}}{-16}
$