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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x+3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-2x)/8x^2+12x/8x^2-3-2=0

We add all the numbers together, and all the variables

(-2x)/8x^2+12x/8x^2-5=0

We multiply all the terms by the denominator


(-2x)+12x-5*8x^2=0

We add all the numbers together, and all the variables

12x+(-2x)-5*8x^2=0

Wy multiply elements

-40x^2+12x+(-2x)=0

We get rid of parentheses

-40x^2+12x-2x=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{-20}{-80}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-40}=\frac{0}{-80}
=0
$