3/d+3=4d+12

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

3/d+3=4d+12

We move all terms to the left:

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


Domain of the equation: d!=0

d∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-9d-4d*d+3=0

Wy multiply elements

-4d^2-9d+3=0

a = -4; b = -9; c = +3;
Δ = b2-4ac
Δ = -92-4·(-4)·3
Δ = 129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{129}}{2*-4}=\frac{9-\sqrt{129}}{-8}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{129}}{2*-4}=\frac{9+\sqrt{129}}{-8}
$