x-3/2x=48-4x

Solution for x-3/2x=48-4x equation:

x-3/2x=48-4x

We move all terms to the left:

x-3/2x-(48-4x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

x-3/2x-(-4x+48)=0

We get rid of parentheses

x-3/2x+4x-48=0

We multiply all the terms by the denominator


x*2x+4x*2x-48*2x-3=0

Wy multiply elements

2x^2+8x^2-96x-3=0

We add all the numbers together, and all the variables

10x^2-96x-3=0

a = 10; b = -96; c = -3;
Δ = b2-4ac
Δ = -962-4·10·(-3)
Δ = 9336
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{9336}=\sqrt{4*2334}=\sqrt{4}*\sqrt{2334}=2\sqrt{2334}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-2\sqrt{2334}}{2*10}=\frac{96-2\sqrt{2334}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+2\sqrt{2334}}{2*10}=\frac{96+2\sqrt{2334}}{20}
$