Solve using the quadratic formula: #4x^2+8x=-3#
To use the quadratic formula, the equation must be in the form
#ax^2+bx+c=0#
Add 3 to both sides to get all the terms on the left.
#4x^2+8xcolor(white)(aaa)=-3#
#color(white)(aaaaaaa)+3color(white)(aaa)+3#
#color(red)4x^2+color(blue)8x+color(magenta)3=0#
#color(red)a=color(red)4, color(blue)b=color(blue)8, color(magenta)c=color(magenta)3#
The quadratic formula is
#x=frac{-color(blue)b+-sqrt(color(blue)b^2-4color(red)acolor(magenta)c)}{2color(red)a}#
#x=frac{-color(blue)8+-sqrt(color(blue)(8)^2-4(color(red)4)(color(magenta)3))}{2(color(red)4)}#
#x=frac{-8+-sqrt(64-48)}{8}#
#x=frac{-8+-sqrt(16)}{8}#
#x=(-8+-4)/8#
Separate into two equations, one with a plus in the numerator and the other with a minus.
#x=(-8+4)/8color(white)(aaaa)x=(-8-4)/8#
#x=(-4)/8color(white)(aaaaaaa)x=(-12)/8#
#x=-1/2color(white)(aaaaaaaa)x=-3/2#
