4/7d-45=d-9

Solution for 4/7d-45=d-9 equation:

4/7d-45=d-9

We move all terms to the left:

4/7d-45-(d-9)=0


Domain of the equation: 7d!=0

d!=0/7

d!=0

d∈R


We get rid of parentheses

4/7d-d+9-45=0

We multiply all the terms by the denominator


-d*7d+9*7d-45*7d+4=0

Wy multiply elements

-7d^2+63d-315d+4=0

We add all the numbers together, and all the variables

-7d^2-252d+4=0

a = -7; b = -252; c = +4;
Δ = b2-4ac
Δ = -2522-4·(-7)·4
Δ = 63616
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:

$\sqrt{\Delta}=\sqrt{63616}=\sqrt{64*994}=\sqrt{64}*\sqrt{994}=8\sqrt{994}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-252)-8\sqrt{994}}{2*-7}=\frac{252-8\sqrt{994}}{-14}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-252)+8\sqrt{994}}{2*-7}=\frac{252+8\sqrt{994}}{-14}
$