6d+15=1/2d-29

Solution for 6d+15=1/2d-29 equation:

6d+15=1/2d-29

We move all terms to the left:

6d+15-(1/2d-29)=0


Domain of the equation: 2d-29)!=0

d∈R


We get rid of parentheses

6d-1/2d+29+15=0

We multiply all the terms by the denominator


6d*2d+29*2d+15*2d-1=0

Wy multiply elements

12d^2+58d+30d-1=0

We add all the numbers together, and all the variables

12d^2+88d-1=0

a = 12; b = 88; c = -1;
Δ = b2-4ac
Δ = 882-4·12·(-1)
Δ = 7792
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:

$\sqrt{\Delta}=\sqrt{7792}=\sqrt{16*487}=\sqrt{16}*\sqrt{487}=4\sqrt{487}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(88)-4\sqrt{487}}{2*12}=\frac{-88-4\sqrt{487}}{24}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(88)+4\sqrt{487}}{2*12}=\frac{-88+4\sqrt{487}}{24}
$