-1/2x-4=5/4x+3

Solution for -1/2x-4=5/4x+3 equation:

-1/2x-4=5/4x+3

We move all terms to the left:

-1/2x-4-(5/4x+3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x+3)!=0

x∈R


We get rid of parentheses

-1/2x-5/4x-3-4=0

We calculate fractions


(-4x)/8x^2+(-10x)/8x^2-3-4=0

We add all the numbers together, and all the variables

(-4x)/8x^2+(-10x)/8x^2-7=0

We multiply all the terms by the denominator


(-4x)+(-10x)-7*8x^2=0

Wy multiply elements

-56x^2+(-4x)+(-10x)=0

We get rid of parentheses

-56x^2-4x-10x=0

We add all the numbers together, and all the variables

-56x^2-14x=0

a = -56; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·(-56)·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*-56}=\frac{0}{-112}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*-56}=\frac{28}{-112}
=-1/4
$