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6x^2+7=217
We move all terms to the left:
6x^2+7-(217)=0
We add all the numbers together, and all the variables
6x^2-210=0
a = 6; b = 0; c = -210;
Δ = b2-4ac
Δ = 02-4·6·(-210)
Δ = 5040
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5040}=\sqrt{144*35}=\sqrt{144}*\sqrt{35}=12\sqrt{35}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{35}}{2*6}=\frac{0-12\sqrt{35}}{12} =-\frac{12\sqrt{35}}{12} =-\sqrt{35} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{35}}{2*6}=\frac{0+12\sqrt{35}}{12} =\frac{12\sqrt{35}}{12} =\sqrt{35} $
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