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3x(2x-7)=9
We move all terms to the left:
3x(2x-7)-(9)=0
We multiply parentheses
6x^2-21x-9=0
a = 6; b = -21; c = -9;
Δ = b2-4ac
Δ = -212-4·6·(-9)
Δ = 657
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{657}=\sqrt{9*73}=\sqrt{9}*\sqrt{73}=3\sqrt{73}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{73}}{2*6}=\frac{21-3\sqrt{73}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{73}}{2*6}=\frac{21+3\sqrt{73}}{12} $
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