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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

(-6x)/8x^2+(-4x)/8x^2-5=0

We multiply all the terms by the denominator


(-6x)+(-4x)-5*8x^2=0

Wy multiply elements

-40x^2+(-6x)+(-4x)=0

We get rid of parentheses

-40x^2-6x-4x=0

We add all the numbers together, and all the variables

-40x^2-10x=0

a = -40; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·(-40)·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*-40}=\frac{0}{-80}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*-40}=\frac{20}{-80}
=-1/4
$