2x^2-9x+4=4x^2-4x+1

Solution for 2x^2-9x+4=4x^2-4x+1 equation:

2x^2-9x+4=4x^2-4x+1

We move all terms to the left:

2x^2-9x+4-(4x^2-4x+1)=0

We get rid of parentheses

2x^2-4x^2-9x+4x-1+4=0

We add all the numbers together, and all the variables

-2x^2-5x+3=0

a = -2; b = -5; c = +3;
Δ = b2-4ac
Δ = -52-4·(-2)·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{-(-5)-7}{2*-2}=\frac{-2}{-4}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+7}{2*-2}=\frac{12}{-4}
=-3
$