5/4x-9=3/2x+14

Solution for 5/4x-9=3/2x+14 equation:

5/4x-9=3/2x+14

We move all terms to the left:

5/4x-9-(3/2x+14)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x+14)!=0

x∈R


We get rid of parentheses

5/4x-3/2x-14-9=0

We calculate fractions


10x/8x^2+(-12x)/8x^2-14-9=0

We add all the numbers together, and all the variables

10x/8x^2+(-12x)/8x^2-23=0

We multiply all the terms by the denominator


10x+(-12x)-23*8x^2=0

Wy multiply elements

-184x^2+10x+(-12x)=0

We get rid of parentheses

-184x^2+10x-12x=0

We add all the numbers together, and all the variables

-184x^2-2x=0

a = -184; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-184)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-184}=\frac{0}{-368}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-184}=\frac{4}{-368}
=-1/92
$