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6x^2=12x+31
We move all terms to the left:
6x^2-(12x+31)=0
We get rid of parentheses
6x^2-12x-31=0
a = 6; b = -12; c = -31;
Δ = b2-4ac
Δ = -122-4·6·(-31)
Δ = 888
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{888}=\sqrt{4*222}=\sqrt{4}*\sqrt{222}=2\sqrt{222}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{222}}{2*6}=\frac{12-2\sqrt{222}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{222}}{2*6}=\frac{12+2\sqrt{222}}{12} $
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