2d-1=3/4d+9

Solution for 2d-1=3/4d+9 equation:

2d-1=3/4d+9

We move all terms to the left:

2d-1-(3/4d+9)=0


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

d∈R


We get rid of parentheses

2d-3/4d-9-1=0

We multiply all the terms by the denominator


2d*4d-9*4d-1*4d-3=0

Wy multiply elements

8d^2-36d-4d-3=0

We add all the numbers together, and all the variables

8d^2-40d-3=0

a = 8; b = -40; c = -3;
Δ = b2-4ac
Δ = -402-4·8·(-3)
Δ = 1696
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:

$\sqrt{\Delta}=\sqrt{1696}=\sqrt{16*106}=\sqrt{16}*\sqrt{106}=4\sqrt{106}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{106}}{2*8}=\frac{40-4\sqrt{106}}{16}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{106}}{2*8}=\frac{40+4\sqrt{106}}{16}
$