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x(6x-1)=25
We move all terms to the left:
x(6x-1)-(25)=0
We multiply parentheses
6x^2-1x-25=0
a = 6; b = -1; c = -25;
Δ = b2-4ac
Δ = -12-4·6·(-25)
Δ = 601
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{-(-1)-\sqrt{601}}{2*6}=\frac{1-\sqrt{601}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{601}}{2*6}=\frac{1+\sqrt{601}}{12} $
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