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(3x-5)(6x-2)=
We move all terms to the left:
(3x-5)(6x-2)-()=0
We add all the numbers together, and all the variables
(3x-5)(6x-2)=0
We multiply parentheses ..
(+18x^2-6x-30x+10)=0
We get rid of parentheses
18x^2-6x-30x+10=0
We add all the numbers together, and all the variables
18x^2-36x+10=0
a = 18; b = -36; c = +10;
Δ = b2-4ac
Δ = -362-4·18·10
Δ = 576
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{576}=24$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-24}{2*18}=\frac{12}{36} =1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+24}{2*18}=\frac{60}{36} =1+2/3 $
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