3/5x-15x=25

Solution for 3/5x-15x=25 equation:

3/5x-15x=25

We move all terms to the left:

3/5x-15x-(25)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-15x+3/5x-25=0

We multiply all the terms by the denominator


-15x*5x-25*5x+3=0

Wy multiply elements

-75x^2-125x+3=0

a = -75; b = -125; c = +3;
Δ = b2-4ac
Δ = -1252-4·(-75)·3
Δ = 16525
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:

$\sqrt{\Delta}=\sqrt{16525}=\sqrt{25*661}=\sqrt{25}*\sqrt{661}=5\sqrt{661}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-125)-5\sqrt{661}}{2*-75}=\frac{125-5\sqrt{661}}{-150}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-125)+5\sqrt{661}}{2*-75}=\frac{125+5\sqrt{661}}{-150}
$