13/4x=18-1/2x

Solution for 13/4x=18-1/2x equation:

13/4x=18-1/2x

We move all terms to the left:

13/4x-(18-1/2x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

13/4x-(-1/2x+18)=0

We get rid of parentheses

13/4x+1/2x-18=0

We calculate fractions


26x/8x^2+4x/8x^2-18=0

We multiply all the terms by the denominator


26x+4x-18*8x^2=0

We add all the numbers together, and all the variables

30x-18*8x^2=0

Wy multiply elements

-144x^2+30x=0

a = -144; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·(-144)·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30}{2*-144}=\frac{-60}{-288}
=5/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*-144}=\frac{0}{-288}
=0
$