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5y(y-2)=35
We move all terms to the left:
5y(y-2)-(35)=0
We multiply parentheses
5y^2-10y-35=0
a = 5; b = -10; c = -35;
Δ = b2-4ac
Δ = -102-4·5·(-35)
Δ = 800
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-20\sqrt{2}}{2*5}=\frac{10-20\sqrt{2}}{10} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+20\sqrt{2}}{2*5}=\frac{10+20\sqrt{2}}{10} $
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