6/7x+1/5x=19/35

Solution for 6/7x+1/5x=19/35 equation:

6/7x+1/5x=19/35

We move all terms to the left:

6/7x+1/5x-(19/35)=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+1/5x-(+19/35)=0

We get rid of parentheses

6/7x+1/5x-19/35=0

We calculate fractions


(-3325x^2)/3675x^2+3150x/3675x^2+735x/3675x^2=0

We multiply all the terms by the denominator


(-3325x^2)+3150x+735x=0

We add all the numbers together, and all the variables

(-3325x^2)+3885x=0

We get rid of parentheses

-3325x^2+3885x=0

a = -3325; b = 3885; c = 0;
Δ = b2-4ac
Δ = 38852-4·(-3325)·0
Δ = 15093225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15093225}=3885$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3885)-3885}{2*-3325}=\frac{-7770}{-6650}
=1+16/95
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3885)+3885}{2*-3325}=\frac{0}{-6650}
=0
$