2/7x+3=3/5x-18

Solution for 2/7x+3=3/5x-18 equation:

2/7x+3=3/5x-18

We move all terms to the left:

2/7x+3-(3/5x-18)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 5x-18)!=0

x∈R


We get rid of parentheses

2/7x-3/5x+18+3=0

We calculate fractions


10x/35x^2+(-21x)/35x^2+18+3=0

We add all the numbers together, and all the variables

10x/35x^2+(-21x)/35x^2+21=0

We multiply all the terms by the denominator


10x+(-21x)+21*35x^2=0

Wy multiply elements

735x^2+10x+(-21x)=0

We get rid of parentheses

735x^2+10x-21x=0

We add all the numbers together, and all the variables

735x^2-11x=0

a = 735; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·735·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*735}=\frac{0}{1470}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*735}=\frac{22}{1470}
=11/735
$