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-2y+3=-3y(2y+7)
We move all terms to the left:
-2y+3-(-3y(2y+7))=0
We calculate terms in parentheses: -(-3y(2y+7)), so:We get rid of parentheses
-3y(2y+7)
We multiply parentheses
-6y^2-21y
Back to the equation:
-(-6y^2-21y)
6y^2+21y-2y+3=0
We add all the numbers together, and all the variables
6y^2+19y+3=0
a = 6; b = 19; c = +3;
Δ = b2-4ac
Δ = 192-4·6·3
Δ = 289
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{289}=17$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-17}{2*6}=\frac{-36}{12} =-3 $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+17}{2*6}=\frac{-2}{12} =-1/6 $
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