8/3d+35=-5/6d+46

Solution for 8/3d+35=-5/6d+46 equation:

8/3d+35=-5/6d+46

We move all terms to the left:

8/3d+35-(-5/6d+46)=0


Domain of the equation: 3d!=0

d!=0/3

d!=0

d∈R



Domain of the equation: 6d+46)!=0

d∈R


We get rid of parentheses

8/3d+5/6d-46+35=0

We calculate fractions


48d/18d^2+15d/18d^2-46+35=0

We add all the numbers together, and all the variables

48d/18d^2+15d/18d^2-11=0

We multiply all the terms by the denominator


48d+15d-11*18d^2=0

We add all the numbers together, and all the variables

63d-11*18d^2=0

Wy multiply elements

-198d^2+63d=0

a = -198; b = 63; c = 0;
Δ = b2-4ac
Δ = 632-4·(-198)·0
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-63}{2*-198}=\frac{-126}{-396}
=7/22
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+63}{2*-198}=\frac{0}{-396}
=0
$