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6(2y+6)=4(9+3y)12y+36=36+12y^12y=12y
We move all terms to the left:
6(2y+6)-(4(9+3y)12y+36)=0
We add all the numbers together, and all the variables
6(2y+6)-(4(3y+9)12y+36)=0
We multiply parentheses
12y-(4(3y+9)12y+36)+36=0
We calculate terms in parentheses: -(4(3y+9)12y+36), so:We get rid of parentheses
4(3y+9)12y+36
We multiply parentheses
144y^2+432y+36
Back to the equation:
-(144y^2+432y+36)
-144y^2+12y-432y-36+36=0
We add all the numbers together, and all the variables
-144y^2-420y=0
a = -144; b = -420; c = 0;
Δ = b2-4ac
Δ = -4202-4·(-144)·0
Δ = 176400
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{176400}=420$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-420)-420}{2*-144}=\frac{0}{-288} =0 $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-420)+420}{2*-144}=\frac{840}{-288} =-2+11/12 $
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