5x-17/3x=-6

Solution for 5x-17/3x=-6 equation:

5x-17/3x=-6

We move all terms to the left:

5x-17/3x-(-6)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

5x-17/3x+6=0

We multiply all the terms by the denominator


5x*3x+6*3x-17=0

Wy multiply elements

15x^2+18x-17=0

a = 15; b = 18; c = -17;
Δ = b2-4ac
Δ = 182-4·15·(-17)
Δ = 1344
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:

$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-8\sqrt{21}}{2*15}=\frac{-18-8\sqrt{21}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+8\sqrt{21}}{2*15}=\frac{-18+8\sqrt{21}}{30}
$