5d=-3+3/4d

Solution for 5d=-3+3/4d equation:

5d=-3+3/4d

We move all terms to the left:

5d-(-3+3/4d)=0


Domain of the equation: 4d)!=0

d!=0/1

d!=0

d∈R


We add all the numbers together, and all the variables

5d-(3/4d-3)=0

We get rid of parentheses

5d-3/4d+3=0

We multiply all the terms by the denominator


5d*4d+3*4d-3=0

Wy multiply elements

20d^2+12d-3=0

a = 20; b = 12; c = -3;
Δ = b2-4ac
Δ = 122-4·20·(-3)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8\sqrt{6}}{2*20}=\frac{-12-8\sqrt{6}}{40}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8\sqrt{6}}{2*20}=\frac{-12+8\sqrt{6}}{40}
$