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9x^2=6x+17
We move all terms to the left:
9x^2-(6x+17)=0
We get rid of parentheses
9x^2-6x-17=0
a = 9; b = -6; c = -17;
Δ = b2-4ac
Δ = -62-4·9·(-17)
Δ = 648
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-18\sqrt{2}}{2*9}=\frac{6-18\sqrt{2}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+18\sqrt{2}}{2*9}=\frac{6+18\sqrt{2}}{18} $
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