3x/7x+35=15-2x

Solution for 3x/7x+35=15-2x equation:

3x/7x+35=15-2x

We move all terms to the left:

3x/7x+35-(15-2x)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

3x/7x-(-2x+15)+35=0

We get rid of parentheses

3x/7x+2x-15+35=0

We multiply all the terms by the denominator


3x+2x*7x-15*7x+35*7x=0

Wy multiply elements

14x^2+3x-105x+245x=0

We add all the numbers together, and all the variables

14x^2+143x=0

a = 14; b = 143; c = 0;
Δ = b2-4ac
Δ = 1432-4·14·0
Δ = 20449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20449}=143$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(143)-143}{2*14}=\frac{-286}{28}
=-10+3/14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(143)+143}{2*14}=\frac{0}{28}
=0
$