3d+5=6(1/2d+1)

Solution for 3d+5=6(1/2d+1) equation:

3d+5=6(1/2d+1)

We move all terms to the left:

3d+5-(6(1/2d+1))=0


Domain of the equation: 2d+1))!=0

d∈R


We multiply all the terms by the denominator


3d*2d+5*2d+1))-(6(1+1))=0

We add all the numbers together, and all the variables

3d*2d+5*2d+1))-(62)=0

We add all the numbers together, and all the variables

3d*2d+5*2d=0

Wy multiply elements

6d^2+10d=0

a = 6; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·6·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*6}=\frac{-20}{12}
=-1+2/3
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*6}=\frac{0}{12}
=0
$