d+(2d+1)+4d+(4d+8)+3/4(4d)=121

Solution for d+(2d+1)+4d+(4d+8)+3/4(4d)=121 equation:

d+(2d+1)+4d+(4d+8)+3/4(4d)=121

We move all terms to the left:

d+(2d+1)+4d+(4d+8)+3/4(4d)-(121)=0


Domain of the equation: 44d!=0

d!=0/44

d!=0

d∈R


We add all the numbers together, and all the variables

5d+(2d+1)+(4d+8)+3/44d-121=0

We get rid of parentheses

5d+2d+4d+3/44d+1+8-121=0

We multiply all the terms by the denominator


5d*44d+2d*44d+4d*44d+1*44d+8*44d-121*44d+3=0

Wy multiply elements

220d^2+88d^2+176d^2+44d+352d-5324d+3=0

We add all the numbers together, and all the variables

484d^2-4928d+3=0

a = 484; b = -4928; c = +3;
Δ = b2-4ac
Δ = -49282-4·484·3
Δ = 24279376
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:

$\sqrt{\Delta}=\sqrt{24279376}=\sqrt{1936*12541}=\sqrt{1936}*\sqrt{12541}=44\sqrt{12541}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4928)-44\sqrt{12541}}{2*484}=\frac{4928-44\sqrt{12541}}{968}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4928)+44\sqrt{12541}}{2*484}=\frac{4928+44\sqrt{12541}}{968}
$