d=3/4d+12

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

d=3/4d+12

We move all terms to the left:

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


Domain of the equation: 4d+12)!=0

d∈R


We get rid of parentheses

d-3/4d-12=0

We multiply all the terms by the denominator


d*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 = 2352
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:

$\sqrt{\Delta}=\sqrt{2352}=\sqrt{784*3}=\sqrt{784}*\sqrt{3}=28\sqrt{3}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-28\sqrt{3}}{2*4}=\frac{48-28\sqrt{3}}{8}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+28\sqrt{3}}{2*4}=\frac{48+28\sqrt{3}}{8}
$