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12x(x-3)=6x+18
We move all terms to the left:
12x(x-3)-(6x+18)=0
We multiply parentheses
12x^2-36x-(6x+18)=0
We get rid of parentheses
12x^2-36x-6x-18=0
We add all the numbers together, and all the variables
12x^2-42x-18=0
a = 12; b = -42; c = -18;
Δ = b2-4ac
Δ = -422-4·12·(-18)
Δ = 2628
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2628}=\sqrt{36*73}=\sqrt{36}*\sqrt{73}=6\sqrt{73}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-6\sqrt{73}}{2*12}=\frac{42-6\sqrt{73}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+6\sqrt{73}}{2*12}=\frac{42+6\sqrt{73}}{24} $
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