( 6x - 4) ( x + 2 ) = 2 ( 11x - 19 ) +2 ( 3^2 -13)

Hier noch einmal die beiden Ergebnisse

der quadratischen Gleichung

(6x-4)*(x+2) = 2*(11x-19)+2*(3²-13)

6x² - 14x + 38 = 0

Gruß radix !

(6x - 4)*(x + 2 ) =2* (11x-19) +2*(3² - 13)

6x²+12x-4x-8 = 22x -38 + 2*(-4)

6x²+12x-4x-22x-8+38+8= 0

6x² -14x +38 = 0            Lösung mit der  a-b-c-Formel (Mitternachtsformel):

x1  = $${\frac{\left({\mathtt{14}}{\mathtt{\,\small\textbf+\,}}{\sqrt{{{\mathtt{14}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{38}}}}\right)}{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{6}}\right)}} = {\frac{{\mathtt{7}}}{{\mathtt{6}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2.229\: \!848\: \!026\: \!711\: \!233\: \!4}}{i}$$     = $${\frac{\left({\mathtt{7}}{\mathtt{\,\small\textbf+\,}}{i}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{179}}}}\right)}{{\mathtt{6}}}}$$

x2   = $${\frac{\left({\mathtt{7}}{\mathtt{\,-\,}}{i}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{179}}}}\right)}{{\mathtt{6}}}}$$

Gruß radix !