3/2x-6=60-48x

Solution for 3/2x-6=60-48x equation:

3/2x-6=60-48x

We move all terms to the left:

3/2x-6-(60-48x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3/2x-(-48x+60)-6=0

We get rid of parentheses

3/2x+48x-60-6=0

We multiply all the terms by the denominator


48x*2x-60*2x-6*2x+3=0

Wy multiply elements

96x^2-120x-12x+3=0

We add all the numbers together, and all the variables

96x^2-132x+3=0

a = 96; b = -132; c = +3;
Δ = b2-4ac
Δ = -1322-4·96·3
Δ = 16272
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:

$\sqrt{\Delta}=\sqrt{16272}=\sqrt{144*113}=\sqrt{144}*\sqrt{113}=12\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-132)-12\sqrt{113}}{2*96}=\frac{132-12\sqrt{113}}{192}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-132)+12\sqrt{113}}{2*96}=\frac{132+12\sqrt{113}}{192}
$