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9x^2-12x+4=28
We move all terms to the left:
9x^2-12x+4-(28)=0
We add all the numbers together, and all the variables
9x^2-12x-24=0
a = 9; b = -12; c = -24;
Δ = b2-4ac
Δ = -122-4·9·(-24)
Δ = 1008
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{7}}{2*9}=\frac{12-12\sqrt{7}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{7}}{2*9}=\frac{12+12\sqrt{7}}{18} $
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