3x-17/5x=-2

Solution for 3x-17/5x=-2 equation:

3x-17/5x=-2

We move all terms to the left:

3x-17/5x-(-2)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

3x-17/5x+2=0

We multiply all the terms by the denominator


3x*5x+2*5x-17=0

Wy multiply elements

15x^2+10x-17=0

a = 15; b = 10; c = -17;
Δ = b2-4ac
Δ = 102-4·15·(-17)
Δ = 1120
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:

$\sqrt{\Delta}=\sqrt{1120}=\sqrt{16*70}=\sqrt{16}*\sqrt{70}=4\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4\sqrt{70}}{2*15}=\frac{-10-4\sqrt{70}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4\sqrt{70}}{2*15}=\frac{-10+4\sqrt{70}}{30}
$