6.7(x^2-3x+2)=x^2

Solution for 6.7(x^2-3x+2)=x^2 equation:

6.7(x^2-3x+2)=x^2

We move all terms to the left:

6.7(x^2-3x+2)-(x^2)=0

determiningTheFunctionDomain
-x^2+6.7(x^2-3x+2)=0

We add all the numbers together, and all the variables

-1x^2+6.7(x^2-3x+2)=0

We multiply parentheses

-1x^2+6.7x^2-20.1x+13.4=0

We add all the numbers together, and all the variables

5.7x^2-20.1x+13.4=0

a = 5.7; b = -20.1; c = +13.4;
Δ = b2-4ac
Δ = -20.12-4·5.7·13.4
Δ = 98.49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20.1)-\sqrt{98.49}}{2*5.7}=\frac{20.1-\sqrt{98.49}}{11.4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20.1)+\sqrt{98.49}}{2*5.7}=\frac{20.1+\sqrt{98.49}}{11.4}
$