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

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
$