3/5x-1-10x=12

Solution for 3/5x-1-10x=12 equation:

3/5x-1-10x=12

We move all terms to the left:

3/5x-1-10x-(12)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-10x+3/5x-13=0

We multiply all the terms by the denominator


-10x*5x-13*5x+3=0

Wy multiply elements

-50x^2-65x+3=0

a = -50; b = -65; c = +3;
Δ = b2-4ac
Δ = -652-4·(-50)·3
Δ = 4825
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:

$\sqrt{\Delta}=\sqrt{4825}=\sqrt{25*193}=\sqrt{25}*\sqrt{193}=5\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-65)-5\sqrt{193}}{2*-50}=\frac{65-5\sqrt{193}}{-100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+5\sqrt{193}}{2*-50}=\frac{65+5\sqrt{193}}{-100}
$