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

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

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

We move all terms to the left:

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


Domain of the equation: 1*7x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

-17x-5(x+12)/1*7x+34-8=0

We multiply all the terms by the denominator


-17x*1*7x-5(x+12)+34*1*7x-8*1*7x=0

We multiply parentheses

-17x*1*7x-5x+34*1*7x-8*1*7x-60=0

Wy multiply elements

-119x^2*7-5x+238x*7-56x*7-60=0

Wy multiply elements

-833x^2-5x+1666x-392x-60=0

We add all the numbers together, and all the variables

-833x^2+1269x-60=0

a = -833; b = 1269; c = -60;
Δ = b2-4ac
Δ = 12692-4·(-833)·(-60)
Δ = 1410441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1269)-\sqrt{1410441}}{2*-833}=\frac{-1269-\sqrt{1410441}}{-1666}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1269)+\sqrt{1410441}}{2*-833}=\frac{-1269+\sqrt{1410441}}{-1666}
$