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(3x-9)(3x-9)=10
We move all terms to the left:
(3x-9)(3x-9)-(10)=0
We multiply parentheses ..
(+9x^2-27x-27x+81)-10=0
We get rid of parentheses
9x^2-27x-27x+81-10=0
We add all the numbers together, and all the variables
9x^2-54x+71=0
a = 9; b = -54; c = +71;
Δ = b2-4ac
Δ = -542-4·9·71
Δ = 360
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{10}}{2*9}=\frac{54-6\sqrt{10}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{10}}{2*9}=\frac{54+6\sqrt{10}}{18} $
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