1/4x=3/2x-9

Solution for 1/4x=3/2x-9 equation:

1/4x=3/2x-9

We move all terms to the left:

1/4x-(3/2x-9)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x-9)!=0

x∈R


We get rid of parentheses

1/4x-3/2x+9=0

We calculate fractions


2x/8x^2+(-12x)/8x^2+9=0

We multiply all the terms by the denominator


2x+(-12x)+9*8x^2=0

Wy multiply elements

72x^2+2x+(-12x)=0

We get rid of parentheses

72x^2+2x-12x=0

We add all the numbers together, and all the variables

72x^2-10x=0

a = 72; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·72·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*72}=\frac{0}{144}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*72}=\frac{20}{144}
=5/36
$