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: 4*4d!=0

d!=0/1

d!=0

d∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

80d^2*4+32d^2*4+64d^2*4+16d*4+128d*4-1936d*4+3=0

Wy multiply elements

320d^2+128d^2+256d^2+64d+512d-7744d+3=0

We add all the numbers together, and all the variables

704d^2-7168d+3=0

a = 704; b = -7168; c = +3;
Δ = b2-4ac
Δ = -71682-4·704·3
Δ = 51371776
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:

$\sqrt{\Delta}=\sqrt{51371776}=\sqrt{256*200671}=\sqrt{256}*\sqrt{200671}=16\sqrt{200671}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7168)-16\sqrt{200671}}{2*704}=\frac{7168-16\sqrt{200671}}{1408}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7168)+16\sqrt{200671}}{2*704}=\frac{7168+16\sqrt{200671}}{1408}
$