Lg(x -5)^1/2 + lg(2x - 3)^1/2 + 1 = lg30 1 = lg10, lg30 =lg3*10 = lg3 + lg10 = lg3 + 1
ОДЗ х - 5 > 0 x > 5 ОДЗ х > 5
2x - 3 > 0 x > 1.5
lg((x - 5) * (2x - 3))^1/2 = lg3
((x - 5) * (2x - 3))^1/2 = 3
(x - 5)(2x - 3) = 9
2x^2 - 13x +15 - 9 = 0
2x^2 - 13x + 6 = 0
D b^2 - 4ac = (-13)^2 - 4*2*6 = 169 - 48 = 121 > 0
x_1 = (-b + VD)/2a = (13 + V121)/2*2 = (13 + 11)/4 = 24/4 = 6 удовл. ОДЗ
x_2 = (-b - VD) /2a = (13 - 11)/4 = 2/4 = 0.5 не удовл. ОДЗ
Ответ. 6