1/2d-1/4d-5=10

Solution for 1/2d-1/4d-5=10 equation:

1/2d-1/4d-5=10

We move all terms to the left:

1/2d-1/4d-5-(10)=0


Domain of the equation: 2d!=0

d!=0/2

d!=0

d∈R



Domain of the equation: 4d!=0

d!=0/4

d!=0

d∈R


We add all the numbers together, and all the variables

1/2d-1/4d-15=0

We calculate fractions


4d/8d^2+(-2d)/8d^2-15=0

We multiply all the terms by the denominator


4d+(-2d)-15*8d^2=0

Wy multiply elements

-120d^2+4d+(-2d)=0

We get rid of parentheses

-120d^2+4d-2d=0

We add all the numbers together, and all the variables

-120d^2+2d=0

a = -120; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-120)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-120}=\frac{-4}{-240}
=1/60
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-120}=\frac{0}{-240}
=0
$