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9x(x-3)=63
We move all terms to the left:
9x(x-3)-(63)=0
We multiply parentheses
9x^2-27x-63=0
a = 9; b = -27; c = -63;
Δ = b2-4ac
Δ = -272-4·9·(-63)
Δ = 2997
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2997}=\sqrt{81*37}=\sqrt{81}*\sqrt{37}=9\sqrt{37}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-9\sqrt{37}}{2*9}=\frac{27-9\sqrt{37}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+9\sqrt{37}}{2*9}=\frac{27+9\sqrt{37}}{18} $
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