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(4x-7)(2x-3)-(2x-3)(2x-3)=12
We move all terms to the left:
(4x-7)(2x-3)-(2x-3)(2x-3)-(12)=0
We multiply parentheses ..
(+8x^2-12x-14x+21)-(2x-3)(2x-3)-12=0
We get rid of parentheses
8x^2-12x-14x-(2x-3)(2x-3)+21-12=0
We multiply parentheses ..
8x^2-(+4x^2-6x-6x+9)-12x-14x+21-12=0
We add all the numbers together, and all the variables
8x^2-(+4x^2-6x-6x+9)-26x+9=0
We get rid of parentheses
8x^2-4x^2+6x+6x-26x-9+9=0
We add all the numbers together, and all the variables
4x^2-14x=0
a = 4; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·4·0
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*4}=\frac{0}{8} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*4}=\frac{28}{8} =3+1/2 $
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