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2x(11x+1)=239
We move all terms to the left:
2x(11x+1)-(239)=0
We multiply parentheses
22x^2+2x-239=0
a = 22; b = 2; c = -239;
Δ = b2-4ac
Δ = 22-4·22·(-239)
Δ = 21036
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{21036}=\sqrt{4*5259}=\sqrt{4}*\sqrt{5259}=2\sqrt{5259}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{5259}}{2*22}=\frac{-2-2\sqrt{5259}}{44} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{5259}}{2*22}=\frac{-2+2\sqrt{5259}}{44} $
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