17(2-x)/1-7x+5(x+12)/7x-1=8

Solution for 17(2-x)/1-7x+5(x+12)/7x-1=8 equation:

17(2-x)/1-7x+5(x+12)/7x-1=8

We move all terms to the left:

17(2-x)/1-7x+5(x+12)/7x-1-(8)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

17(-1x+2)/1-7x+5(x+12)/7x-1-8=0

We add all the numbers together, and all the variables

-7x+17(-1x+2)/1+5(x+12)/7x-9=0

We calculate fractions


(-119x^2+238x)/7x-7x+(5x+60)/7x-9=0

We multiply all the terms by the denominator


(-119x^2+238x)-7x*7x+(5x+60)-9*7x=0

Wy multiply elements

(-119x^2+238x)-49x^2+(5x+60)-63x=0

We get rid of parentheses

-119x^2-49x^2+238x+5x-63x+60=0

We add all the numbers together, and all the variables

-168x^2+180x+60=0

a = -168; b = 180; c = +60;
Δ = b2-4ac
Δ = 1802-4·(-168)·60
Δ = 72720
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:

$\sqrt{\Delta}=\sqrt{72720}=\sqrt{144*505}=\sqrt{144}*\sqrt{505}=12\sqrt{505}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-12\sqrt{505}}{2*-168}=\frac{-180-12\sqrt{505}}{-336}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+12\sqrt{505}}{2*-168}=\frac{-180+12\sqrt{505}}{-336}
$