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12y+6=6(2y+1)12y+6=6(2y+1)
We move all terms to the left:
12y+6-(6(2y+1)12y+6)=0
We calculate terms in parentheses: -(6(2y+1)12y+6), so:We get rid of parentheses
6(2y+1)12y+6
We multiply parentheses
144y^2+72y+6
Back to the equation:
-(144y^2+72y+6)
-144y^2+12y-72y-6+6=0
We add all the numbers together, and all the variables
-144y^2-60y=0
a = -144; b = -60; c = 0;
Δ = b2-4ac
Δ = -602-4·(-144)·0
Δ = 3600
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{3600}=60$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-60}{2*-144}=\frac{0}{-288} =0 $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+60}{2*-144}=\frac{120}{-288} =-5/12 $
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