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6x^2-x=14
We move all terms to the left:
6x^2-x-(14)=0
We add all the numbers together, and all the variables
6x^2-1x-14=0
a = 6; b = -1; c = -14;
Δ = b2-4ac
Δ = -12-4·6·(-14)
Δ = 337
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{-(-1)-\sqrt{337}}{2*6}=\frac{1-\sqrt{337}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{337}}{2*6}=\frac{1+\sqrt{337}}{12} $
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