5/3x-17=3x-25

Solution for 5/3x-17=3x-25 equation:

5/3x-17=3x-25

We move all terms to the left:

5/3x-17-(3x-25)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

5/3x-3x+25-17=0

We multiply all the terms by the denominator


-3x*3x+25*3x-17*3x+5=0

Wy multiply elements

-9x^2+75x-51x+5=0

We add all the numbers together, and all the variables

-9x^2+24x+5=0

a = -9; b = 24; c = +5;
Δ = b2-4ac
Δ = 242-4·(-9)·5
Δ = 756
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:

$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-6\sqrt{21}}{2*-9}=\frac{-24-6\sqrt{21}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+6\sqrt{21}}{2*-9}=\frac{-24+6\sqrt{21}}{-18}
$