3/5x-9/10x=1

Solution for 3/5x-9/10x=1 equation:

3/5x-9/10x=1

We move all terms to the left:

3/5x-9/10x-(1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We calculate fractions


30x/50x^2+(-45x)/50x^2-1=0

We multiply all the terms by the denominator


30x+(-45x)-1*50x^2=0

Wy multiply elements

-50x^2+30x+(-45x)=0

We get rid of parentheses

-50x^2+30x-45x=0

We add all the numbers together, and all the variables

-50x^2-15x=0

a = -50; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·(-50)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*-50}=\frac{0}{-100}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*-50}=\frac{30}{-100}
=-3/10
$