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(6x-5)(x=2)=0
We move all terms to the left:
(6x-5)(x-(2))=0
We multiply parentheses ..
(+6x^2-12x-5x+10)=0
We get rid of parentheses
6x^2-12x-5x+10=0
We add all the numbers together, and all the variables
6x^2-17x+10=0
a = 6; b = -17; c = +10;
Δ = b2-4ac
Δ = -172-4·6·10
Δ = 49
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{49}=7$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-7}{2*6}=\frac{10}{12} =5/6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+7}{2*6}=\frac{24}{12} =2 $
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