3/2x+8=1/4x-6

Solution for 3/2x+8=1/4x-6 equation:

3/2x+8=1/4x-6

We move all terms to the left:

3/2x+8-(1/4x-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-1/4x+6+8=0

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


12x+(-2x)+14*8x^2=0

Wy multiply elements

112x^2+12x+(-2x)=0

We get rid of parentheses

112x^2+12x-2x=0

We add all the numbers together, and all the variables

112x^2+10x=0

a = 112; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·112·0
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*112}=\frac{-20}{224}
=-5/56
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*112}=\frac{0}{224}
=0
$