129.6+9/5x=288-4x

Solution for 129.6+9/5x=288-4x equation:

129.6+9/5x=288-4x

We move all terms to the left:

129.6+9/5x-(288-4x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

9/5x-(-4x+288)+129.6=0

We get rid of parentheses

9/5x+4x-288+129.6=0

We multiply all the terms by the denominator


4x*5x-288*5x+(129.6)*5x+9=0

We multiply parentheses

4x*5x-288*5x+648x+9=0

Wy multiply elements

20x^2-1440x+648x+9=0

We add all the numbers together, and all the variables

20x^2-792x+9=0

a = 20; b = -792; c = +9;
Δ = b2-4ac
Δ = -7922-4·20·9
Δ = 626544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{626544}=\sqrt{144*4351}=\sqrt{144}*\sqrt{4351}=12\sqrt{4351}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-792)-12\sqrt{4351}}{2*20}=\frac{792-12\sqrt{4351}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-792)+12\sqrt{4351}}{2*20}=\frac{792+12\sqrt{4351}}{40}
$