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3x(x-2)=121
We move all terms to the left:
3x(x-2)-(121)=0
We multiply parentheses
3x^2-6x-121=0
a = 3; b = -6; c = -121;
Δ = b2-4ac
Δ = -62-4·3·(-121)
Δ = 1488
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1488}=\sqrt{16*93}=\sqrt{16}*\sqrt{93}=4\sqrt{93}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{93}}{2*3}=\frac{6-4\sqrt{93}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{93}}{2*3}=\frac{6+4\sqrt{93}}{6} $
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