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x(x+5)=46
We move all terms to the left:
x(x+5)-(46)=0
We multiply parentheses
x^2+5x-46=0
a = 1; b = 5; c = -46;
Δ = b2-4ac
Δ = 52-4·1·(-46)
Δ = 209
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{-(5)-\sqrt{209}}{2*1}=\frac{-5-\sqrt{209}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{209}}{2*1}=\frac{-5+\sqrt{209}}{2} $
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