3/2x+2=5/4x-6

Solution for 3/2x+2=5/4x-6 equation:

3/2x+2=5/4x-6

We move all terms to the left:

3/2x+2-(5/4x-6)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x-6)!=0

x∈R


We get rid of parentheses

3/2x-5/4x+6+2=0

We calculate fractions


12x/8x^2+(-10x)/8x^2+6+2=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

64x^2+12x+(-10x)=0

We get rid of parentheses

64x^2+12x-10x=0

We add all the numbers together, and all the variables

64x^2+2x=0

a = 64; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·64·0
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*64}=\frac{-4}{128}
=-1/32
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*64}=\frac{0}{128}
=0
$