Answer
$x=4, 20$
Work Step by Step
$\sqrt {2x-4} - \sqrt{3x+4} =-2$
$\sqrt {2x-4} - \sqrt{3x+4}+\sqrt{3x+4} =-2+\sqrt{3x+4}$
$\sqrt {2x-4} =-2+\sqrt{3x+4}$
$\sqrt {2x-4} =\sqrt{3x+4}-2$
$(\sqrt {2x-4})^2 =(\sqrt{3x+4}-2)^2$
$2x-4 = \sqrt{3x+4}*\sqrt{3x+4}+\sqrt{3x+4}*(-2)+(-2)*\sqrt{3x+4})+(-2)(-2)$
$2x-4 = (3x+4)-4\sqrt{3x+4}+(-2)(-2)$
$2x-4 = (3x+4)-4\sqrt{3x+4}+4$
$2x-4 = 3x+4-4\sqrt{3x+4}+4$
$2x-4 = 3x+8-4\sqrt{3x+4}$
$-x-4 = 8-4\sqrt{3x+4}$
$-x-12 = -4\sqrt{3x+4}$
$(-x-12)/-4 = -4\sqrt{3x+4}/-4$
$.25x+3 =\sqrt{3x+4}$
$(.25x+3)^2 =(\sqrt{3x+4})^2$
$(1/4*x)^2+.25x*3+3*.25x+3*3=3x+4$
$1/16x^2+1.5x+9=3x+4$
$1/16x^2-1.5x+5=0$
$16*(1/16x^2-1.5x+5=0)$
$x^2-24x+80=0$
$(x-4)(x-20)=0$
$x-4=0$
$x=4$
$x-20=0$
$x=20$
$x=4$
$\sqrt {2x-4} - \sqrt{3x+4} =-2$
$\sqrt {2*4-4} - \sqrt{3*4+4} =-2$
$\sqrt {8-4} - \sqrt{12+4} =-2$
$\sqrt {4} - \sqrt{16} =-2$
$2 -4=-2$
$-2=-2$ (true)
$x=20$
$\sqrt {2x-4} - \sqrt{3x+4} =-2$
$\sqrt {2*20-4} - \sqrt{3*20+4} =-2$
$\sqrt {40-4} - \sqrt{3*20+4} =-2$
$\sqrt {36} - \sqrt{60+4} =-2$
$6 - \sqrt {64} =-2$
$6-8=-2$
$-2=-2$ (true)
