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6x^2-13x-7=2
We move all terms to the left:
6x^2-13x-7-(2)=0
We add all the numbers together, and all the variables
6x^2-13x-9=0
a = 6; b = -13; c = -9;
Δ = b2-4ac
Δ = -132-4·6·(-9)
Δ = 385
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{-(-13)-\sqrt{385}}{2*6}=\frac{13-\sqrt{385}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{385}}{2*6}=\frac{13+\sqrt{385}}{12} $
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