-4/5x=12+2/15x

Solution for -4/5x=12+2/15x equation:

-4/5x=12+2/15x

We move all terms to the left:

-4/5x-(12+2/15x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 15x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-4/5x-(2/15x+12)=0

We get rid of parentheses

-4/5x-2/15x-12=0

We calculate fractions


(-60x)/75x^2+(-10x)/75x^2-12=0

We multiply all the terms by the denominator


(-60x)+(-10x)-12*75x^2=0

Wy multiply elements

-900x^2+(-60x)+(-10x)=0

We get rid of parentheses

-900x^2-60x-10x=0

We add all the numbers together, and all the variables

-900x^2-70x=0

a = -900; b = -70; c = 0;
Δ = b2-4ac
Δ = -702-4·(-900)·0
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-70}{2*-900}=\frac{0}{-1800}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+70}{2*-900}=\frac{140}{-1800}
=-7/90
$