Определите значения x, при которых верно равенство: (x-3)^2/16 - (x-2)^2/4 = (1-x)/2

[latex] \frac{(x-3) ^{2} }{16} - \frac{(x-2) ^{2} }{4} = \frac{1-x}{2} |*16[/latex] [latex](x-3) ^{2} -4(x-2) ^{2} =8(1-x)[/latex] [latex] x^{2} -6x+9-4( x^{2} -4x+4)=8-8x[/latex] [latex] x^{2} -6x+9-4 x^{2} +16x-16=8-8x[/latex] [latex]-3 x^{2} +18x-15=0|:(-3) [/latex] [latex] x^{2} -6x+5=0[/latex] D = (-6)² - 4·1·5 = 36 - 20 = 16 [latex] \sqrt{D}=4 [/latex] [latex] x_{1} = \frac{6+4}{2} = \frac{10}{2} =5[/latex] [latex] x_{2} = \frac{6-4}{2}= \frac{2}{2} =1[/latex]