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6x(3x-11)=74
We move all terms to the left:
6x(3x-11)-(74)=0
We multiply parentheses
18x^2-66x-74=0
a = 18; b = -66; c = -74;
Δ = b2-4ac
Δ = -662-4·18·(-74)
Δ = 9684
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9684}=\sqrt{36*269}=\sqrt{36}*\sqrt{269}=6\sqrt{269}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-6\sqrt{269}}{2*18}=\frac{66-6\sqrt{269}}{36} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+6\sqrt{269}}{2*18}=\frac{66+6\sqrt{269}}{36} $
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