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

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

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

We move all terms to the left:

-1/4x+8-(3/2x-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

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

112x^2-14x=0

a = 112; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·112·0
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*112}=\frac{0}{224}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*112}=\frac{28}{224}
=1/8
$