3/4x+18=12x-42

Solution for 3/4x+18=12x-42 equation:

3/4x+18=12x-42

We move all terms to the left:

3/4x+18-(12x-42)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/4x-12x+42+18=0

We multiply all the terms by the denominator


-12x*4x+42*4x+18*4x+3=0

Wy multiply elements

-48x^2+168x+72x+3=0

We add all the numbers together, and all the variables

-48x^2+240x+3=0

a = -48; b = 240; c = +3;
Δ = b2-4ac
Δ = 2402-4·(-48)·3
Δ = 58176
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:

$\sqrt{\Delta}=\sqrt{58176}=\sqrt{576*101}=\sqrt{576}*\sqrt{101}=24\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-24\sqrt{101}}{2*-48}=\frac{-240-24\sqrt{101}}{-96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+24\sqrt{101}}{2*-48}=\frac{-240+24\sqrt{101}}{-96}
$