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6x(6x-1)=24
We move all terms to the left:
6x(6x-1)-(24)=0
We multiply parentheses
36x^2-6x-24=0
a = 36; b = -6; c = -24;
Δ = b2-4ac
Δ = -62-4·36·(-24)
Δ = 3492
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3492}=\sqrt{36*97}=\sqrt{36}*\sqrt{97}=6\sqrt{97}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{97}}{2*36}=\frac{6-6\sqrt{97}}{72} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{97}}{2*36}=\frac{6+6\sqrt{97}}{72} $
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