3/7x-1-9/5x=-83/35

Solution for 3/7x-1-9/5x=-83/35 equation:

3/7x-1-9/5x=-83/35

We move all terms to the left:

3/7x-1-9/5x-(-83/35)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

3/7x-9/5x-1+83/35=0

We calculate fractions


14525x^2/3675x^2+1575x/3675x^2+(-6615x)/3675x^2-1=0

We multiply all the terms by the denominator


14525x^2+1575x+(-6615x)-1*3675x^2=0

Wy multiply elements

14525x^2-3675x^2+1575x+(-6615x)=0

We get rid of parentheses

14525x^2-3675x^2+1575x-6615x=0

We add all the numbers together, and all the variables

10850x^2-5040x=0

a = 10850; b = -5040; c = 0;
Δ = b2-4ac
Δ = -50402-4·10850·0
Δ = 25401600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25401600}=5040$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5040)-5040}{2*10850}=\frac{0}{21700}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5040)+5040}{2*10850}=\frac{10080}{21700}
=72/155
$