X-27=9/5y

Solution for X-27=9/5y equation:

X-27=9/5X

We move all terms to the left:

X-27-(9/5X)=0


Domain of the equation: 5X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(+9/5X)-27=0

We get rid of parentheses

X-9/5X-27=0

We multiply all the terms by the denominator


X*5X-27*5X-9=0

Wy multiply elements

5X^2-135X-9=0

a = 5; b = -135; c = -9;
Δ = b2-4ac
Δ = -1352-4·5·(-9)
Δ = 18405
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{18405}=\sqrt{9*2045}=\sqrt{9}*\sqrt{2045}=3\sqrt{2045}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-135)-3\sqrt{2045}}{2*5}=\frac{135-3\sqrt{2045}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-135)+3\sqrt{2045}}{2*5}=\frac{135+3\sqrt{2045}}{10}
$