1/2d+5=3d

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

1/2d+5=3d

We move all terms to the left:

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


Domain of the equation: 2d!=0

d!=0/2

d!=0

d∈R


We add all the numbers together, and all the variables

-3d+1/2d+5=0

We multiply all the terms by the denominator


-3d*2d+5*2d+1=0

Wy multiply elements

-6d^2+10d+1=0

a = -6; b = 10; c = +1;
Δ = b2-4ac
Δ = 102-4·(-6)·1
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{31}}{2*-6}=\frac{-10-2\sqrt{31}}{-12}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{31}}{2*-6}=\frac{-10+2\sqrt{31}}{-12}
$