2d-3/5;d=9

Solution for 2d-3/5;d=9 equation:

2d-3/5d=9

We move all terms to the left:

2d-3/5d-(9)=0


Domain of the equation: 5d!=0

d!=0/5

d!=0

d∈R


We multiply all the terms by the denominator


2d*5d-9*5d-3=0

Wy multiply elements

10d^2-45d-3=0

a = 10; b = -45; c = -3;
Δ = b2-4ac
Δ = -452-4·10·(-3)
Δ = 2145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-\sqrt{2145}}{2*10}=\frac{45-\sqrt{2145}}{20}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2145}}{2*10}=\frac{45+\sqrt{2145}}{20}
$