the quadtratic formula is based on standard form equation: #color(red)(a)x^2+color(blue)(b)x+color(green)(c)#:
#(-color(blue)(b)+-sqrt(color(blue)(b)^2+4xxcolor(red)(a)xxcolor(green)(c)))/(2xxcolor(red)(a))#
So, we have #7x^2+7=12x#. First, we need to reorder this into Standard Form:
#7x^2+7=12x#
#7x^2-12x+7=0#
Now we have #color(red)(7)x^2+color(blue)(-12)x+color(green)(7)#
That gives us
#(-color(blue)((-12))+-sqrt(color(blue)((-12))^2+4xxcolor(red)((7))xxcolor(green)((7))))/(2xxcolor(red)((7)))#
I like to use parentheses. It keeps everything in order.
Now we just simplify:
#(12+-sqrt(144+196))/(14)#
#(12+-sqrt(340))/(14)#
#(12+-2sqrt(85))/(14)#
#(6+-sqrt(85))/(7)#
That means #x=(6+sqrt(84))/7# or #~~2.174#
and #x=x=(6-sqrt(84))/7# or #~~-0.459#
