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9x^2+54x=7
We move all terms to the left:
9x^2+54x-(7)=0
a = 9; b = 54; c = -7;
Δ = b2-4ac
Δ = 542-4·9·(-7)
Δ = 3168
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3168}=\sqrt{144*22}=\sqrt{144}*\sqrt{22}=12\sqrt{22}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-12\sqrt{22}}{2*9}=\frac{-54-12\sqrt{22}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+12\sqrt{22}}{2*9}=\frac{-54+12\sqrt{22}}{18} $
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