d+1/2d=3+7

Solution for d+1/2d=3+7 equation:

d+1/2d=3+7

We move all terms to the left:

d+1/2d-(3+7)=0


Domain of the equation: 2d!=0

d!=0/2

d!=0

d∈R


We add all the numbers together, and all the variables

d+1/2d-10=0

We multiply all the terms by the denominator


d*2d-10*2d+1=0

Wy multiply elements

2d^2-20d+1=0

a = 2; b = -20; c = +1;
Δ = b2-4ac
Δ = -202-4·2·1
Δ = 392
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:

$\sqrt{\Delta}=\sqrt{392}=\sqrt{196*2}=\sqrt{196}*\sqrt{2}=14\sqrt{2}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-14\sqrt{2}}{2*2}=\frac{20-14\sqrt{2}}{4}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+14\sqrt{2}}{2*2}=\frac{20+14\sqrt{2}}{4}
$