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x(x-11)=3
We move all terms to the left:
x(x-11)-(3)=0
We multiply parentheses
x^2-11x-3=0
a = 1; b = -11; c = -3;
Δ = b2-4ac
Δ = -112-4·1·(-3)
Δ = 133
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{-(-11)-\sqrt{133}}{2*1}=\frac{11-\sqrt{133}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{133}}{2*1}=\frac{11+\sqrt{133}}{2} $
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