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(3x-18)(3x-9)=6x-15
We move all terms to the left:
(3x-18)(3x-9)-(6x-15)=0
We get rid of parentheses
(3x-18)(3x-9)-6x+15=0
We multiply parentheses ..
(+9x^2-27x-54x+162)-6x+15=0
We get rid of parentheses
9x^2-27x-54x-6x+162+15=0
We add all the numbers together, and all the variables
9x^2-87x+177=0
a = 9; b = -87; c = +177;
Δ = b2-4ac
Δ = -872-4·9·177
Δ = 1197
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1197}=\sqrt{9*133}=\sqrt{9}*\sqrt{133}=3\sqrt{133}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-87)-3\sqrt{133}}{2*9}=\frac{87-3\sqrt{133}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-87)+3\sqrt{133}}{2*9}=\frac{87+3\sqrt{133}}{18} $
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