(2/d-5)-(6/4d+9)+(4/d-5)=0

Solution for (2/d-5)-(6/4d+9)+(4/d-5)=0 equation:

(2/d-5)-(6/4d+9)+(4/d-5)=0


Domain of the equation: d-5)!=0

d∈R



Domain of the equation: 4d+9)!=0

d∈R


We get rid of parentheses

2/d-6/4d+4/d-5-9-5=0

We calculate fractions


(16d+2)/4d^2+(-6d)/4d^2-5-9-5=0

We add all the numbers together, and all the variables

(16d+2)/4d^2+(-6d)/4d^2-19=0

We multiply all the terms by the denominator


(16d+2)+(-6d)-19*4d^2=0

Wy multiply elements

-76d^2+(16d+2)+(-6d)=0

We get rid of parentheses

-76d^2+16d-6d+2=0

We add all the numbers together, and all the variables

-76d^2+10d+2=0

a = -76; b = 10; c = +2;
Δ = b2-4ac
Δ = 102-4·(-76)·2
Δ = 708
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:

$\sqrt{\Delta}=\sqrt{708}=\sqrt{4*177}=\sqrt{4}*\sqrt{177}=2\sqrt{177}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{177}}{2*-76}=\frac{-10-2\sqrt{177}}{-152}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{177}}{2*-76}=\frac{-10+2\sqrt{177}}{-152}
$