First, let's un-factor the left side of the equation. Our equation should be #x^2+4x+3# = 84. We need to get the right side to equal 0, so let's subtract 84 from both sides. The equation should be #x^2+4x-81# = 0. Now, we can try to factor the equation, but it won't be possible. Since we can't factor it, let's plug in the quadratic equation. Refresher: the quadratic equation is x = #(-b±sqrt(b^2-4ac))/(2a)# . In this equation, our a=1 b=4 and c= -81. Now, let's plug it all in. Our new equation will be x = #(-4±sqrt((4^2)-4(1*-81)))/(2*1)#. After simplifying, we get #(-4±sqrt(16-(4*-81)))/2#. Simplify even further and we get #(-4±sqrt(16-(-324)))/2#. We will add 16 and 84 since subtracting a negative number is equal to adding a positive number. Our new equation is #(-4±sqrt(340))/2#. 340 is equal to 4 times 85. 4 is a perfect square (its square root is 2). So, our new equation is #(-4±sqrt4 sqrt85)/2# which simplifies to #(-4±2sqrt85)/2#. Both terms on the top can be divided by 2, so our new equation (and answer) is #-2±sqrt85#
