1/(8)x+56=4x+140

Solution for 1/(8)x+56=4x+140 equation:

1/(8)x+56=4x+140

We move all terms to the left:

1/(8)x+56-(4x+140)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We get rid of parentheses

1/8x-4x-140+56=0

We multiply all the terms by the denominator


-4x*8x-140*8x+56*8x+1=0

Wy multiply elements

-32x^2-1120x+448x+1=0

We add all the numbers together, and all the variables

-32x^2-672x+1=0

a = -32; b = -672; c = +1;
Δ = b2-4ac
Δ = -6722-4·(-32)·1
Δ = 451712
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:

$\sqrt{\Delta}=\sqrt{451712}=\sqrt{64*7058}=\sqrt{64}*\sqrt{7058}=8\sqrt{7058}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-672)-8\sqrt{7058}}{2*-32}=\frac{672-8\sqrt{7058}}{-64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-672)+8\sqrt{7058}}{2*-32}=\frac{672+8\sqrt{7058}}{-64}
$