(3x-1)(-2x+3)=0

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Solution for (3x-1)(-2x+3)=0 equation:



(3x-1)(-2x+3)=0
We multiply parentheses ..
(-6x^2+9x+2x-3)=0
We get rid of parentheses
-6x^2+9x+2x-3=0
We add all the numbers together, and all the variables
-6x^2+11x-3=0
a = -6; b = 11; c = -3;
Δ = b2-4ac
Δ = 112-4·(-6)·(-3)
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{-(11)-7}{2*-6}=\frac{-18}{-12} =1+1/2 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+7}{2*-6}=\frac{-4}{-12} =1/3 $

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