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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x-6)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


6x/8x^2+(-20x)/8x^2+6+2=0

We add all the numbers together, and all the variables

6x/8x^2+(-20x)/8x^2+8=0

We multiply all the terms by the denominator


6x+(-20x)+8*8x^2=0

Wy multiply elements

64x^2+6x+(-20x)=0

We get rid of parentheses

64x^2+6x-20x=0

We add all the numbers together, and all the variables

64x^2-14x=0

a = 64; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·64·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*64}=\frac{0}{128}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*64}=\frac{28}{128}
=7/32
$