4/55d-9+12d+4+d-6+2d=271

Solution for 4/55d-9+12d+4+d-6+2d=271 equation:

4/55d-9+12d+4+d-6+2d=271

We move all terms to the left:

4/55d-9+12d+4+d-6+2d-(271)=0


Domain of the equation: 55d!=0

d!=0/55

d!=0

d∈R


We add all the numbers together, and all the variables

15d+4/55d-282=0

We multiply all the terms by the denominator


15d*55d-282*55d+4=0

Wy multiply elements

825d^2-15510d+4=0

a = 825; b = -15510; c = +4;
Δ = b2-4ac
Δ = -155102-4·825·4
Δ = 240546900
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:

$\sqrt{\Delta}=\sqrt{240546900}=\sqrt{100*2405469}=\sqrt{100}*\sqrt{2405469}=10\sqrt{2405469}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15510)-10\sqrt{2405469}}{2*825}=\frac{15510-10\sqrt{2405469}}{1650}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15510)+10\sqrt{2405469}}{2*825}=\frac{15510+10\sqrt{2405469}}{1650}
$