4-1/5x=10-11/15x

Solution for 4-1/5x=10-11/15x equation:

4-1/5x=10-11/15x

We move all terms to the left:

4-1/5x-(10-11/15x)=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

-1/5x-(-11/15x+10)+4=0

We get rid of parentheses

-1/5x+11/15x-10+4=0

We calculate fractions


(-15x)/75x^2+55x/75x^2-10+4=0

We add all the numbers together, and all the variables

(-15x)/75x^2+55x/75x^2-6=0

We multiply all the terms by the denominator


(-15x)+55x-6*75x^2=0

We add all the numbers together, and all the variables

55x+(-15x)-6*75x^2=0

Wy multiply elements

-450x^2+55x+(-15x)=0

We get rid of parentheses

-450x^2+55x-15x=0

We add all the numbers together, and all the variables

-450x^2+40x=0

a = -450; b = 40; c = 0;
Δ = b2-4ac
Δ = 402-4·(-450)·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-40}{2*-450}=\frac{-80}{-900}
=4/45
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+40}{2*-450}=\frac{0}{-900}
=0
$