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x(2x+1)=81
We move all terms to the left:
x(2x+1)-(81)=0
We multiply parentheses
2x^2+x-81=0
a = 2; b = 1; c = -81;
Δ = b2-4ac
Δ = 12-4·2·(-81)
Δ = 649
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{649}}{2*2}=\frac{-1-\sqrt{649}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{649}}{2*2}=\frac{-1+\sqrt{649}}{4} $
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