3/4d=12-d

Solution for 3/4d=12-d equation:

3/4d=12-d

We move all terms to the left:

3/4d-(12-d)=0


Domain of the equation: 4d!=0

d!=0/4

d!=0

d∈R


We add all the numbers together, and all the variables

3/4d-(-1d+12)=0

We get rid of parentheses

3/4d+1d-12=0

We multiply all the terms by the denominator


1d*4d-12*4d+3=0

Wy multiply elements

4d^2-48d+3=0

a = 4; b = -48; c = +3;
Δ = b2-4ac
Δ = -482-4·4·3
Δ = 2256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2256}=\sqrt{16*141}=\sqrt{16}*\sqrt{141}=4\sqrt{141}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{141}}{2*4}=\frac{48-4\sqrt{141}}{8}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{141}}{2*4}=\frac{48+4\sqrt{141}}{8}
$