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(4x-2)(x-3)+3(2x-3)(2-4x)=0
We add all the numbers together, and all the variables
(4x-2)(x-3)+3(2x-3)(-4x+2)=0
We multiply parentheses ..
(+4x^2-12x-2x+6)+3(2x-3)(-4x+2)=0
We get rid of parentheses
4x^2-12x-2x+3(2x-3)(-4x+2)+6=0
We multiply parentheses ..
4x^2+3(-8x^2+4x+12x-6)-12x-2x+6=0
We add all the numbers together, and all the variables
4x^2+3(-8x^2+4x+12x-6)-14x+6=0
We multiply parentheses
4x^2-24x^2+12x+36x-14x-18+6=0
We add all the numbers together, and all the variables
-20x^2+34x-12=0
a = -20; b = 34; c = -12;
Δ = b2-4ac
Δ = 342-4·(-20)·(-12)
Δ = 196
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{196}=14$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-14}{2*-20}=\frac{-48}{-40} =1+1/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+14}{2*-20}=\frac{-20}{-40} =1/2 $
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