-1/5x+7=2/3x-4

Solution for -1/5x+7=2/3x-4 equation:

-1/5x+7=2/3x-4

We move all terms to the left:

-1/5x+7-(2/3x-4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x-4)!=0

x∈R


We get rid of parentheses

-1/5x-2/3x+4+7=0

We calculate fractions


(-3x)/15x^2+(-10x)/15x^2+4+7=0

We add all the numbers together, and all the variables

(-3x)/15x^2+(-10x)/15x^2+11=0

We multiply all the terms by the denominator


(-3x)+(-10x)+11*15x^2=0

Wy multiply elements

165x^2+(-3x)+(-10x)=0

We get rid of parentheses

165x^2-3x-10x=0

We add all the numbers together, and all the variables

165x^2-13x=0

a = 165; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·165·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*165}=\frac{0}{330}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*165}=\frac{26}{330}
=13/165
$