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y(y-6)=10
We move all terms to the left:
y(y-6)-(10)=0
We multiply parentheses
y^2-6y-10=0
a = 1; b = -6; c = -10;
Δ = b2-4ac
Δ = -62-4·1·(-10)
Δ = 76
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{19}}{2*1}=\frac{6-2\sqrt{19}}{2} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{19}}{2*1}=\frac{6+2\sqrt{19}}{2} $
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