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8x^2-18x=9
We move all terms to the left:
8x^2-18x-(9)=0
a = 8; b = -18; c = -9;
Δ = b2-4ac
Δ = -182-4·8·(-9)
Δ = 612
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{612}=\sqrt{36*17}=\sqrt{36}*\sqrt{17}=6\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{17}}{2*8}=\frac{18-6\sqrt{17}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{17}}{2*8}=\frac{18+6\sqrt{17}}{16} $
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