2/3-3/2y+1/3y=-4

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Solution for 2/3-3/2y+1/3y=-4 equation:



2/3-3/2y+1/3y=-4
We move all terms to the left:
2/3-3/2y+1/3y-(-4)=0
Domain of the equation: 2y!=0
y!=0/2
y!=0
y∈R
Domain of the equation: 3y!=0
y!=0/3
y!=0
y∈R
We add all the numbers together, and all the variables
-3/2y+1/3y+4+2/3=0
We calculate fractions
(-81y)/54y^2+2y/54y^2+4y/54y^2+4=0
We multiply all the terms by the denominator
(-81y)+2y+4y+4*54y^2=0
We add all the numbers together, and all the variables
6y+(-81y)+4*54y^2=0
Wy multiply elements
216y^2+6y+(-81y)=0
We get rid of parentheses
216y^2+6y-81y=0
We add all the numbers together, and all the variables
216y^2-75y=0
a = 216; b = -75; c = 0;
Δ = b2-4ac
Δ = -752-4·216·0
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-75}{2*216}=\frac{0}{432} =0 $
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+75}{2*216}=\frac{150}{432} =25/72 $

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