3/2x+5=9/4x-11

Solution for 3/2x+5=9/4x-11 equation:

3/2x+5=9/4x-11

We move all terms to the left:

3/2x+5-(9/4x-11)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x-11)!=0

x∈R


We get rid of parentheses

3/2x-9/4x+11+5=0

We calculate fractions


12x/8x^2+(-18x)/8x^2+11+5=0

We add all the numbers together, and all the variables

12x/8x^2+(-18x)/8x^2+16=0

We multiply all the terms by the denominator


12x+(-18x)+16*8x^2=0

Wy multiply elements

128x^2+12x+(-18x)=0

We get rid of parentheses

128x^2+12x-18x=0

We add all the numbers together, and all the variables

128x^2-6x=0

a = 128; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·128·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*128}=\frac{0}{256}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*128}=\frac{12}{256}
=3/64
$