8x-4/3x+17=17x-23

Solution for 8x-4/3x+17=17x-23 equation:

8x-4/3x+17=17x-23

We move all terms to the left:

8x-4/3x+17-(17x-23)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

8x-4/3x-17x+23+17=0

We multiply all the terms by the denominator


8x*3x-17x*3x+23*3x+17*3x-4=0

Wy multiply elements

24x^2-51x^2+69x+51x-4=0

We add all the numbers together, and all the variables

-27x^2+120x-4=0

a = -27; b = 120; c = -4;
Δ = b2-4ac
Δ = 1202-4·(-27)·(-4)
Δ = 13968
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:

$\sqrt{\Delta}=\sqrt{13968}=\sqrt{144*97}=\sqrt{144}*\sqrt{97}=12\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-12\sqrt{97}}{2*-27}=\frac{-120-12\sqrt{97}}{-54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+12\sqrt{97}}{2*-27}=\frac{-120+12\sqrt{97}}{-54}
$