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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



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

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-2/5x-2/3x-1-1=0

We calculate fractions


(-6x)/15x^2+(-10x)/15x^2-1-1=0

We add all the numbers together, and all the variables

(-6x)/15x^2+(-10x)/15x^2-2=0

We multiply all the terms by the denominator


(-6x)+(-10x)-2*15x^2=0

Wy multiply elements

-30x^2+(-6x)+(-10x)=0

We get rid of parentheses

-30x^2-6x-10x=0

We add all the numbers together, and all the variables

-30x^2-16x=0

a = -30; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·(-30)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*-30}=\frac{0}{-60}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*-30}=\frac{32}{-60}
=-8/15
$