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0=6x^2+17x+9
We move all terms to the left:
0-(6x^2+17x+9)=0
We add all the numbers together, and all the variables
-(6x^2+17x+9)=0
We get rid of parentheses
-6x^2-17x-9=0
a = -6; b = -17; c = -9;
Δ = b2-4ac
Δ = -172-4·(-6)·(-9)
Δ = 73
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{-(-17)-\sqrt{73}}{2*-6}=\frac{17-\sqrt{73}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{73}}{2*-6}=\frac{17+\sqrt{73}}{-12} $
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