2/3*d-5/8*d=26

Solution for 2/3*d-5/8*d=26 equation:

2/3d-5/8d=26

We move all terms to the left:

2/3d-5/8d-(26)=0


Domain of the equation: 3d!=0

d!=0/3

d!=0

d∈R



Domain of the equation: 8d!=0

d!=0/8

d!=0

d∈R


We calculate fractions


16d/24d^2+(-15d)/24d^2-26=0

We multiply all the terms by the denominator


16d+(-15d)-26*24d^2=0

Wy multiply elements

-624d^2+16d+(-15d)=0

We get rid of parentheses

-624d^2+16d-15d=0

We add all the numbers together, and all the variables

-624d^2+d=0

a = -624; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-624)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-624}=\frac{-2}{-1248}
=1/624
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-624}=\frac{0}{-1248}
=0
$