4/9x-8/5x=87

Solution for 4/9x-8/5x=87 equation:

4/9x-8/5x=87

We move all terms to the left:

4/9x-8/5x-(87)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We calculate fractions


20x/45x^2+(-72x)/45x^2-87=0

We multiply all the terms by the denominator


20x+(-72x)-87*45x^2=0

Wy multiply elements

-3915x^2+20x+(-72x)=0

We get rid of parentheses

-3915x^2+20x-72x=0

We add all the numbers together, and all the variables

-3915x^2-52x=0

a = -3915; b = -52; c = 0;
Δ = b2-4ac
Δ = -522-4·(-3915)·0
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-52}{2*-3915}=\frac{0}{-7830}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+52}{2*-3915}=\frac{104}{-7830}
=-52/3915
$