-3Y=18x-20/3X

Solution for -3Y=18x-20/3X equation:

-3=18Y-20/3Y

We move all terms to the left:

-3-(18Y-20/3Y)=0


Domain of the equation: 3Y)!=0

Y!=0/1

Y!=0

Y∈R


We add all the numbers together, and all the variables

-(+18Y-20/3Y)-3=0

We get rid of parentheses

-18Y+20/3Y-3=0

We multiply all the terms by the denominator


-18Y*3Y-3*3Y+20=0

Wy multiply elements

-54Y^2-9Y+20=0

a = -54; b = -9; c = +20;
Δ = b2-4ac
Δ = -92-4·(-54)·20
Δ = 4401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4401}=\sqrt{9*489}=\sqrt{9}*\sqrt{489}=3\sqrt{489}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{489}}{2*-54}=\frac{9-3\sqrt{489}}{-108}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{489}}{2*-54}=\frac{9+3\sqrt{489}}{-108}
$