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5x(6x-1)=1
We move all terms to the left:
5x(6x-1)-(1)=0
We multiply parentheses
30x^2-5x-1=0
a = 30; b = -5; c = -1;
Δ = b2-4ac
Δ = -52-4·30·(-1)
Δ = 145
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{-(-5)-\sqrt{145}}{2*30}=\frac{5-\sqrt{145}}{60} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{145}}{2*30}=\frac{5+\sqrt{145}}{60} $
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