3/4x+24=x-12

Solution for 3/4x+24=x-12 equation:

3/4x+24=x-12

We move all terms to the left:

3/4x+24-(x-12)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/4x-x+12+24=0

We multiply all the terms by the denominator


-x*4x+12*4x+24*4x+3=0

Wy multiply elements

-4x^2+48x+96x+3=0

We add all the numbers together, and all the variables

-4x^2+144x+3=0

a = -4; b = 144; c = +3;
Δ = b2-4ac
Δ = 1442-4·(-4)·3
Δ = 20784
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:

$\sqrt{\Delta}=\sqrt{20784}=\sqrt{16*1299}=\sqrt{16}*\sqrt{1299}=4\sqrt{1299}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-4\sqrt{1299}}{2*-4}=\frac{-144-4\sqrt{1299}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+4\sqrt{1299}}{2*-4}=\frac{-144+4\sqrt{1299}}{-8}
$