[tex]5x+3y-17=0\\5x+3y=17\\3y=17-5x /:3\\y=-\frac{5}3x+\frac{17}3\\\\x^2+(-\frac53x+\frac{17}3)^2=17\\x^2+(\frac{25}9x^2-\frac{170}9x+\frac{289}9)=17\\x^2+\frac{25}9x^2-\frac{170}9x+\frac{289}9=17\\\frac{9}9x^2+\frac{25}9x^2-\frac{170}9x+\frac{289}9=17\\\frac{34x^2-170x+289}9=17 /*9\\34x^2-170x+289=153 /-153\\34x^2-170x+136=0\\\\\Delta=(-170)^2-4*34*136\\\Delta=28900-18496\\\Delta=10404\\\sqrt{\Delta}=102\\\\x_1=\frac{170-102}{68}=\frac{68}{68}=1\\x_2=\frac{170+102}{68}=4\\[/tex]
[tex]y_1=-\frac53*1+\frac{17}3=-\frac53+\frac{17}3=\frac{12}3=4\\y_2=-\frac53*4+\frac{17}3=-\frac{20}3+\frac{17}3=-\frac33=-1[/tex]
A=(1, 4)
B=(4, -1)
