X^2-6x+4=(-x^2)+4x-4

Solution for X^2-6x+4=(-x^2)+4x-4 equation:

X^2-6X+4=(-X^2)+4X-4

We move all terms to the left:

X^2-6X+4-((-X^2)+4X-4)=0


We calculate terms in parentheses: -((-X^2)+4X-4), so:

(-X^2)+4X-4

We get rid of parentheses

-X^2+4X-4

We add all the numbers together, and all the variables

-1X^2+4X-4

Back to the equation:

-(-1X^2+4X-4)


We get rid of parentheses

X^2+1X^2-4X-6X+4+4=0

We add all the numbers together, and all the variables

2X^2-10X+8=0

a = 2; b = -10; c = +8;
Δ = b2-4ac
Δ = -102-4·2·8
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6}{2*2}=\frac{4}{4}
=1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6}{2*2}=\frac{16}{4}
=4
$