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(3x-2)(2x=7)
We move all terms to the left:
(3x-2)(2x-(7))=0
We multiply parentheses ..
(+6x^2-21x-4x+14)=0
We get rid of parentheses
6x^2-21x-4x+14=0
We add all the numbers together, and all the variables
6x^2-25x+14=0
a = 6; b = -25; c = +14;
Δ = b2-4ac
Δ = -252-4·6·14
Δ = 289
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{289}=17$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-17}{2*6}=\frac{8}{12} =2/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+17}{2*6}=\frac{42}{12} =3+1/2 $
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