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2y(y+9)=3(y+9)
We move all terms to the left:
2y(y+9)-(3(y+9))=0
We multiply parentheses
2y^2+18y-(3(y+9))=0
We calculate terms in parentheses: -(3(y+9)), so:We get rid of parentheses
3(y+9)
We multiply parentheses
3y+27
Back to the equation:
-(3y+27)
2y^2+18y-3y-27=0
We add all the numbers together, and all the variables
2y^2+15y-27=0
a = 2; b = 15; c = -27;
Δ = b2-4ac
Δ = 152-4·2·(-27)
Δ = 441
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{441}=21$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-21}{2*2}=\frac{-36}{4} =-9 $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+21}{2*2}=\frac{6}{4} =1+1/2 $
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