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 = 18576
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:

$\sqrt{\Delta}=\sqrt{18576}=\sqrt{144*129}=\sqrt{144}*\sqrt{129}=12\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-132)-12\sqrt{129}}{2*-96}=\frac{132-12\sqrt{129}}{-192}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-132)+12\sqrt{129}}{2*-96}=\frac{132+12\sqrt{129}}{-192}
$