-1/6d+2=7d+45

Solution for -1/6d+2=7d+45 equation:

-1/6d+2=7d+45

We move all terms to the left:

-1/6d+2-(7d+45)=0


Domain of the equation: 6d!=0

d!=0/6

d!=0

d∈R


We get rid of parentheses

-1/6d-7d-45+2=0

We multiply all the terms by the denominator


-7d*6d-45*6d+2*6d-1=0

Wy multiply elements

-42d^2-270d+12d-1=0

We add all the numbers together, and all the variables

-42d^2-258d-1=0

a = -42; b = -258; c = -1;
Δ = b2-4ac
Δ = -2582-4·(-42)·(-1)
Δ = 66396
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:

$\sqrt{\Delta}=\sqrt{66396}=\sqrt{4*16599}=\sqrt{4}*\sqrt{16599}=2\sqrt{16599}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-258)-2\sqrt{16599}}{2*-42}=\frac{258-2\sqrt{16599}}{-84}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-258)+2\sqrt{16599}}{2*-42}=\frac{258+2\sqrt{16599}}{-84}
$