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9y(6y+15)=230
We move all terms to the left:
9y(6y+15)-(230)=0
We multiply parentheses
54y^2+135y-230=0
a = 54; b = 135; c = -230;
Δ = b2-4ac
Δ = 1352-4·54·(-230)
Δ = 67905
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{67905}=\sqrt{9*7545}=\sqrt{9}*\sqrt{7545}=3\sqrt{7545}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(135)-3\sqrt{7545}}{2*54}=\frac{-135-3\sqrt{7545}}{108} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(135)+3\sqrt{7545}}{2*54}=\frac{-135+3\sqrt{7545}}{108} $
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