4/5x-7+1/3x+2=4/5x+9

Solution for 4/5x-7+1/3x+2=4/5x+9 equation:

4/5x-7+1/3x+2=4/5x+9

We move all terms to the left:

4/5x-7+1/3x+2-(4/5x+9)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x+9)!=0

x∈R


We add all the numbers together, and all the variables

4/5x+1/3x-(4/5x+9)-5=0

We get rid of parentheses

4/5x+1/3x-4/5x-9-5=0

We calculate fractions


(-12x+4)/15x^2+5x/15x^2-9-5=0

We add all the numbers together, and all the variables

(-12x+4)/15x^2+5x/15x^2-14=0

We multiply all the terms by the denominator


(-12x+4)+5x-14*15x^2=0

We add all the numbers together, and all the variables

5x+(-12x+4)-14*15x^2=0

Wy multiply elements

-210x^2+5x+(-12x+4)=0

We get rid of parentheses

-210x^2+5x-12x+4=0

We add all the numbers together, and all the variables

-210x^2-7x+4=0

a = -210; b = -7; c = +4;
Δ = b2-4ac
Δ = -72-4·(-210)·4
Δ = 3409
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{3409}}{2*-210}=\frac{7-\sqrt{3409}}{-420}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{3409}}{2*-210}=\frac{7+\sqrt{3409}}{-420}
$