8/3d+35=5/6d+45

Solution for 8/3d+35=5/6d+45 equation:

8/3d+35=5/6d+45

We move all terms to the left:

8/3d+35-(5/6d+45)=0


Domain of the equation: 3d!=0

d!=0/3

d!=0

d∈R



Domain of the equation: 6d+45)!=0

d∈R


We get rid of parentheses

8/3d-5/6d-45+35=0

We calculate fractions


48d/18d^2+(-15d)/18d^2-45+35=0

We add all the numbers together, and all the variables

48d/18d^2+(-15d)/18d^2-10=0

We multiply all the terms by the denominator


48d+(-15d)-10*18d^2=0

Wy multiply elements

-180d^2+48d+(-15d)=0

We get rid of parentheses

-180d^2+48d-15d=0

We add all the numbers together, and all the variables

-180d^2+33d=0

a = -180; b = 33; c = 0;
Δ = b2-4ac
Δ = 332-4·(-180)·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-33}{2*-180}=\frac{-66}{-360}
=11/60
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+33}{2*-180}=\frac{0}{-360}
=0
$