1/8x-3(x-7)=51/8x-3

Solution for 1/8x-3(x-7)=51/8x-3 equation:

1/8x-3(x-7)=51/8x-3

We move all terms to the left:

1/8x-3(x-7)-(51/8x-3)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 8x-3)!=0

x∈R


We multiply parentheses

1/8x-3x-(51/8x-3)+21=0

We get rid of parentheses

1/8x-3x-51/8x+3+21=0

We multiply all the terms by the denominator


-3x*8x+3*8x+21*8x+1-51=0

We add all the numbers together, and all the variables

-3x*8x+3*8x+21*8x-50=0

Wy multiply elements

-24x^2+24x+168x-50=0

We add all the numbers together, and all the variables

-24x^2+192x-50=0

a = -24; b = 192; c = -50;
Δ = b2-4ac
Δ = 1922-4·(-24)·(-50)
Δ = 32064
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:

$\sqrt{\Delta}=\sqrt{32064}=\sqrt{64*501}=\sqrt{64}*\sqrt{501}=8\sqrt{501}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(192)-8\sqrt{501}}{2*-24}=\frac{-192-8\sqrt{501}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(192)+8\sqrt{501}}{2*-24}=\frac{-192+8\sqrt{501}}{-48}
$