(2x+5)^2+(5x-3)^2=75+2x найти корни

Question

(2x+5)^2+(5x-3)^2=75+2x найти корни

Answer 1

4х²+20х+25+25х²-30х+9=75+2х
4х²+20х+25+25х²-30х+9-75-2х=0

29х²-12х-41=0

D=12² - 4×29×(-41)=4900=70²

x1=12+70/58=82/58=1 целая 12/29
x2=12-70/58=-1

Ответ: (-1; 1 целая 12/29)