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(x-2)6x=180
We move all terms to the left:
(x-2)6x-(180)=0
We multiply parentheses
6x^2-12x-180=0
a = 6; b = -12; c = -180;
Δ = b2-4ac
Δ = -122-4·6·(-180)
Δ = 4464
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4464}=\sqrt{144*31}=\sqrt{144}*\sqrt{31}=12\sqrt{31}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{31}}{2*6}=\frac{12-12\sqrt{31}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{31}}{2*6}=\frac{12+12\sqrt{31}}{12} $
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