1/8d-4+3/4d-4=5

Solution for 1/8d-4+3/4d-4=5 equation:

1/8d-4+3/4d-4=5

We move all terms to the left:

1/8d-4+3/4d-4-(5)=0


Domain of the equation: 8d!=0

d!=0/8

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

1/8d+3/4d-13=0

We calculate fractions


4d/32d^2+24d/32d^2-13=0

We multiply all the terms by the denominator


4d+24d-13*32d^2=0

We add all the numbers together, and all the variables

28d-13*32d^2=0

Wy multiply elements

-416d^2+28d=0

a = -416; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·(-416)·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*-416}=\frac{-56}{-832}
=7/104
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*-416}=\frac{0}{-832}
=0
$