8/3x-41/15=-4/5x+1

Solution for 8/3x-41/15=-4/5x+1 equation:

8/3x-41/15=-4/5x+1

We move all terms to the left:

8/3x-41/15-(-4/5x+1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x+1)!=0

x∈R


We get rid of parentheses

8/3x+4/5x-1-41/15=0

We calculate fractions


(-3075x^2)/225x^2+600x/225x^2+180x/225x^2-1=0

We multiply all the terms by the denominator


(-3075x^2)+600x+180x-1*225x^2=0

We add all the numbers together, and all the variables

(-3075x^2)+780x-1*225x^2=0

Wy multiply elements

(-3075x^2)-225x^2+780x=0

We get rid of parentheses

-3075x^2-225x^2+780x=0

We add all the numbers together, and all the variables

-3300x^2+780x=0

a = -3300; b = 780; c = 0;
Δ = b2-4ac
Δ = 7802-4·(-3300)·0
Δ = 608400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{608400}=780$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(780)-780}{2*-3300}=\frac{-1560}{-6600}
=13/55
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(780)+780}{2*-3300}=\frac{0}{-6600}
=0
$