-3/5x+6/5=-1/3x-7

Solution for -3/5x+6/5=-1/3x-7 equation:

-3/5x+6/5=-1/3x-7

We move all terms to the left:

-3/5x+6/5-(-1/3x-7)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x-7)!=0

x∈R


We get rid of parentheses

-3/5x+1/3x+7+6/5=0

We calculate fractions


(-9x)/375x^2+125x/375x^2+18x/375x^2+7=0

We multiply all the terms by the denominator


(-9x)+125x+18x+7*375x^2=0

We add all the numbers together, and all the variables

143x+(-9x)+7*375x^2=0

Wy multiply elements

2625x^2+143x+(-9x)=0

We get rid of parentheses

2625x^2+143x-9x=0

We add all the numbers together, and all the variables

2625x^2+134x=0

a = 2625; b = 134; c = 0;
Δ = b2-4ac
Δ = 1342-4·2625·0
Δ = 17956
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{17956}=134$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(134)-134}{2*2625}=\frac{-268}{5250}
=-134/2625
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(134)+134}{2*2625}=\frac{0}{5250}
=0
$