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6x^2-69x=-104
We move all terms to the left:
6x^2-69x-(-104)=0
We add all the numbers together, and all the variables
6x^2-69x+104=0
a = 6; b = -69; c = +104;
Δ = b2-4ac
Δ = -692-4·6·104
Δ = 2265
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{-(-69)-\sqrt{2265}}{2*6}=\frac{69-\sqrt{2265}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-69)+\sqrt{2265}}{2*6}=\frac{69+\sqrt{2265}}{12} $
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