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-5y(180+5y)=180
We move all terms to the left:
-5y(180+5y)-(180)=0
We add all the numbers together, and all the variables
-5y(5y+180)-180=0
We multiply parentheses
-25y^2-900y-180=0
a = -25; b = -900; c = -180;
Δ = b2-4ac
Δ = -9002-4·(-25)·(-180)
Δ = 792000
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{792000}=\sqrt{14400*55}=\sqrt{14400}*\sqrt{55}=120\sqrt{55}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-900)-120\sqrt{55}}{2*-25}=\frac{900-120\sqrt{55}}{-50} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-900)+120\sqrt{55}}{2*-25}=\frac{900+120\sqrt{55}}{-50} $
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