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3x(2x-7)=1
We move all terms to the left:
3x(2x-7)-(1)=0
We multiply parentheses
6x^2-21x-1=0
a = 6; b = -21; c = -1;
Δ = b2-4ac
Δ = -212-4·6·(-1)
Δ = 465
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-\sqrt{465}}{2*6}=\frac{21-\sqrt{465}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{465}}{2*6}=\frac{21+\sqrt{465}}{12} $
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