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20y^2+120y=135
We move all terms to the left:
20y^2+120y-(135)=0
a = 20; b = 120; c = -135;
Δ = b2-4ac
Δ = 1202-4·20·(-135)
Δ = 25200
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{25200}=\sqrt{3600*7}=\sqrt{3600}*\sqrt{7}=60\sqrt{7}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-60\sqrt{7}}{2*20}=\frac{-120-60\sqrt{7}}{40} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+60\sqrt{7}}{2*20}=\frac{-120+60\sqrt{7}}{40} $
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