5x+(4.5-1/3x)=36

Solution for 5x+(4.5-1/3x)=36 equation:

5x+(4.5-1/3x)=36

We move all terms to the left:

5x+(4.5-1/3x)-(36)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x+(-1/3x+4.5)-36=0

We get rid of parentheses

5x-1/3x+4.5-36=0

We multiply all the terms by the denominator


5x*3x+(4.5)*3x-36*3x-1=0

We multiply parentheses

5x*3x+13.5x-36*3x-1=0

Wy multiply elements

15x^2+13.5x-108x-1=0

We add all the numbers together, and all the variables

15x^2-94.5x-1=0

a = 15; b = -94.5; c = -1;
Δ = b2-4ac
Δ = -94.52-4·15·(-1)
Δ = 8990.25
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{-(-94.5)-\sqrt{8990.25}}{2*15}=\frac{94.5-\sqrt{8990.25}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-94.5)+\sqrt{8990.25}}{2*15}=\frac{94.5+\sqrt{8990.25}}{30}
$