d=10+1/3d

Solution for d=10+1/3d equation:

d=10+1/3d

We move all terms to the left:

d-(10+1/3d)=0


Domain of the equation: 3d)!=0

d!=0/1

d!=0

d∈R


We add all the numbers together, and all the variables

d-(1/3d+10)=0

We get rid of parentheses

d-1/3d-10=0

We multiply all the terms by the denominator


d*3d-10*3d-1=0

Wy multiply elements

3d^2-30d-1=0

a = 3; b = -30; c = -1;
Δ = b2-4ac
Δ = -302-4·3·(-1)
Δ = 912
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:

$\sqrt{\Delta}=\sqrt{912}=\sqrt{16*57}=\sqrt{16}*\sqrt{57}=4\sqrt{57}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-4\sqrt{57}}{2*3}=\frac{30-4\sqrt{57}}{6}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+4\sqrt{57}}{2*3}=\frac{30+4\sqrt{57}}{6}
$