7/8d=49d=

Solution for 7/8d=49d= equation:

7/8d=49d=

We move all terms to the left:

7/8d-(49d)=0


Domain of the equation: 8d!=0

d!=0/8

d!=0

d∈R


We add all the numbers together, and all the variables

-49d+7/8d=0

We multiply all the terms by the denominator


-49d*8d+7=0

Wy multiply elements

-392d^2+7=0

a = -392; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-392)·7
Δ = 10976
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:

$\sqrt{\Delta}=\sqrt{10976}=\sqrt{784*14}=\sqrt{784}*\sqrt{14}=28\sqrt{14}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-28\sqrt{14}}{2*-392}=\frac{0-28\sqrt{14}}{-784}
=-\frac{28\sqrt{14}}{-784}
=-\frac{\sqrt{14}}{-28}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28\sqrt{14}}{2*-392}=\frac{0+28\sqrt{14}}{-784}
=\frac{28\sqrt{14}}{-784}
=\frac{\sqrt{14}}{-28}
$