4x2-12x+9=(2x-3)2

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Solution for 4x2-12x+9=(2x-3)2 equation:



4x^2-12x+9=(2x-3)2
We move all terms to the left:
4x^2-12x+9-((2x-3)2)=0
We calculate terms in parentheses: -((2x-3)2), so:
(2x-3)2
We multiply parentheses
4x-6
Back to the equation:
-(4x-6)
We get rid of parentheses
4x^2-12x-4x+6+9=0
We add all the numbers together, and all the variables
4x^2-16x+15=0
a = 4; b = -16; c = +15;
Δ = b2-4ac
Δ = -162-4·4·15
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4}{2*4}=\frac{12}{8} =1+1/2 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4}{2*4}=\frac{20}{8} =2+1/2 $

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