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

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

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

We move all terms to the left:

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


Domain of the equation: 5d!=0

d!=0/5

d!=0

d∈R



Domain of the equation: 8d!=0

d!=0/8

d!=0

d∈R


We add all the numbers together, and all the variables

1/5d+3/8d-13=0

We calculate fractions


8d/40d^2+15d/40d^2-13=0

We multiply all the terms by the denominator


8d+15d-13*40d^2=0

We add all the numbers together, and all the variables

23d-13*40d^2=0

Wy multiply elements

-520d^2+23d=0

a = -520; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·(-520)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*-520}=\frac{-46}{-1040}
=23/520
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*-520}=\frac{0}{-1040}
=0
$