Idon’t understand how to do number 38

The two red angle markers (the arcs) indicate that we have congruent angles. So this is an isosceles triangle making the two sides 24 and x^2+5x to be equal in length

Set the expressions equal to each other and solve for x
x^2+5x = 24
x^2+5x-24 = 0
(x-3)(x+8) = 0
x-3=0 or x+8=0
x = 3 or x = -8

So x is either 3 or -8
Plugging either x value into x^2+5x will have it turn into 24