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5(3x-2)6x=-1
We move all terms to the left:
5(3x-2)6x-(-1)=0
We add all the numbers together, and all the variables
5(3x-2)6x+1=0
We multiply parentheses
90x^2-60x+1=0
a = 90; b = -60; c = +1;
Δ = b2-4ac
Δ = -602-4·90·1
Δ = 3240
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3240}=\sqrt{324*10}=\sqrt{324}*\sqrt{10}=18\sqrt{10}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-18\sqrt{10}}{2*90}=\frac{60-18\sqrt{10}}{180} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+18\sqrt{10}}{2*90}=\frac{60+18\sqrt{10}}{180} $
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