6/7x+3/5x=17/35

Solution for 6/7x+3/5x=17/35 equation:

6/7x+3/5x=17/35

We move all terms to the left:

6/7x+3/5x-(17/35)=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 add all the numbers together, and all the variables

6/7x+3/5x-(+17/35)=0

We get rid of parentheses

6/7x+3/5x-17/35=0

We calculate fractions


(-2975x^2)/3675x^2+3150x/3675x^2+2205x/3675x^2=0

We multiply all the terms by the denominator


(-2975x^2)+3150x+2205x=0

We add all the numbers together, and all the variables

(-2975x^2)+5355x=0

We get rid of parentheses

-2975x^2+5355x=0

a = -2975; b = 5355; c = 0;
Δ = b2-4ac
Δ = 53552-4·(-2975)·0
Δ = 28676025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{28676025}=5355$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5355)-5355}{2*-2975}=\frac{-10710}{-5950}
=1+4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5355)+5355}{2*-2975}=\frac{0}{-5950}
=0
$