7/2d+6=4d-1

Solution for 7/2d+6=4d-1 equation:

7/2d+6=4d-1

We move all terms to the left:

7/2d+6-(4d-1)=0


Domain of the equation: 2d!=0

d!=0/2

d!=0

d∈R


We get rid of parentheses

7/2d-4d+1+6=0

We multiply all the terms by the denominator


-4d*2d+1*2d+6*2d+7=0

Wy multiply elements

-8d^2+2d+12d+7=0

We add all the numbers together, and all the variables

-8d^2+14d+7=0

a = -8; b = 14; c = +7;
Δ = b2-4ac
Δ = 142-4·(-8)·7
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{105}}{2*-8}=\frac{-14-2\sqrt{105}}{-16}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{105}}{2*-8}=\frac{-14+2\sqrt{105}}{-16}
$