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9x(x+1)=91
We move all terms to the left:
9x(x+1)-(91)=0
We multiply parentheses
9x^2+9x-91=0
a = 9; b = 9; c = -91;
Δ = b2-4ac
Δ = 92-4·9·(-91)
Δ = 3357
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3357}=\sqrt{9*373}=\sqrt{9}*\sqrt{373}=3\sqrt{373}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{373}}{2*9}=\frac{-9-3\sqrt{373}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{373}}{2*9}=\frac{-9+3\sqrt{373}}{18} $
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