5/2x+9=1/4x+54

Solution for 5/2x+9=1/4x+54 equation:

5/2x+9=1/4x+54

We move all terms to the left:

5/2x+9-(1/4x+54)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x+54)!=0

x∈R


We get rid of parentheses

5/2x-1/4x-54+9=0

We calculate fractions


20x/8x^2+(-2x)/8x^2-54+9=0

We add all the numbers together, and all the variables

20x/8x^2+(-2x)/8x^2-45=0

We multiply all the terms by the denominator


20x+(-2x)-45*8x^2=0

Wy multiply elements

-360x^2+20x+(-2x)=0

We get rid of parentheses

-360x^2+20x-2x=0

We add all the numbers together, and all the variables

-360x^2+18x=0

a = -360; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·(-360)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*-360}=\frac{-36}{-720}
=1/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*-360}=\frac{0}{-720}
=0
$