(9/7)d=9/2

Solution for (9/7)d=9/2 equation:

(9/7)d=9/2

We move all terms to the left:

(9/7)d-(9/2)=0


Domain of the equation: 7)d!=0

d!=0/1

d!=0

d∈R


We add all the numbers together, and all the variables

(+9/7)d-(+9/2)=0

We multiply parentheses

9d^2-(+9/2)=0

We get rid of parentheses

9d^2-9/2=0

We multiply all the terms by the denominator


9d^2*2-9=0

Wy multiply elements

18d^2-9=0

a = 18; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·18·(-9)
Δ = 648
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{2}}{2*18}=\frac{0-18\sqrt{2}}{36}
=-\frac{18\sqrt{2}}{36}
=-\frac{\sqrt{2}}{2}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{2}}{2*18}=\frac{0+18\sqrt{2}}{36}
=\frac{18\sqrt{2}}{36}
=\frac{\sqrt{2}}{2}
$