5/7x+7=5/3x+45

Solution for 5/7x+7=5/3x+45 equation:

5/7x+7=5/3x+45

We move all terms to the left:

5/7x+7-(5/3x+45)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 3x+45)!=0

x∈R


We get rid of parentheses

5/7x-5/3x-45+7=0

We calculate fractions


15x/21x^2+(-35x)/21x^2-45+7=0

We add all the numbers together, and all the variables

15x/21x^2+(-35x)/21x^2-38=0

We multiply all the terms by the denominator


15x+(-35x)-38*21x^2=0

Wy multiply elements

-798x^2+15x+(-35x)=0

We get rid of parentheses

-798x^2+15x-35x=0

We add all the numbers together, and all the variables

-798x^2-20x=0

a = -798; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·(-798)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*-798}=\frac{0}{-1596}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*-798}=\frac{40}{-1596}
=-10/399
$