1/8x-3(x-7)=5.125x-3

Solution for 1/8x-3(x-7)=5.125x-3 equation:

1/8x-3(x-7)=5.125x-3

We move all terms to the left:

1/8x-3(x-7)-(5.125x-3)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We multiply parentheses

1/8x-3x-(5.125x-3)+21=0

We get rid of parentheses

1/8x-3x-5.125x+3+21=0

We multiply all the terms by the denominator


-3x*8x-(5.125x)*8x+3*8x+21*8x+1=0

We add all the numbers together, and all the variables

-3x*8x-(+5.125x)*8x+3*8x+21*8x+1=0

We multiply parentheses

-40x^2-3x*8x+3*8x+21*8x+1=0

Wy multiply elements

-40x^2-24x^2+24x+168x+1=0

We add all the numbers together, and all the variables

-64x^2+192x+1=0

a = -64; b = 192; c = +1;
Δ = b2-4ac
Δ = 1922-4·(-64)·1
Δ = 37120
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:

$\sqrt{\Delta}=\sqrt{37120}=\sqrt{256*145}=\sqrt{256}*\sqrt{145}=16\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(192)-16\sqrt{145}}{2*-64}=\frac{-192-16\sqrt{145}}{-128}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(192)+16\sqrt{145}}{2*-64}=\frac{-192+16\sqrt{145}}{-128}
$