-3/5x-7/10x=1

Solution for -3/5x-7/10x=1 equation:

-3/5x-7/10x=1

We move all terms to the left:

-3/5x-7/10x-(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+(-35x)/50x^2-1=0

We multiply all the terms by the denominator


(-30x)+(-35x)-1*50x^2=0

Wy multiply elements

-50x^2+(-30x)+(-35x)=0

We get rid of parentheses

-50x^2-30x-35x=0

We add all the numbers together, and all the variables

-50x^2-65x=0

a = -50; b = -65; c = 0;
Δ = b2-4ac
Δ = -652-4·(-50)·0
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-65)-65}{2*-50}=\frac{0}{-100}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+65}{2*-50}=\frac{130}{-100}
=-1+3/10
$