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x(6x-4)=52
We move all terms to the left:
x(6x-4)-(52)=0
We multiply parentheses
6x^2-4x-52=0
a = 6; b = -4; c = -52;
Δ = b2-4ac
Δ = -42-4·6·(-52)
Δ = 1264
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1264}=\sqrt{16*79}=\sqrt{16}*\sqrt{79}=4\sqrt{79}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{79}}{2*6}=\frac{4-4\sqrt{79}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{79}}{2*6}=\frac{4+4\sqrt{79}}{12} $
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