Solve the quadratic equation.

2x2 + 35 = 17x

Get it to equal 0

minus 17x from both sides

2x²-17x+35=0

tricky part

get something like

(2x-a) (x-b)

we know the signs are negative since the middle term is negative and last term is positive

so a and b are either 1 and 35 or 5 and 7

(2x-1) (x-35), nope

(2x-35) (x-1) nope

(2x-5) (x-7), nope

(2x-7) (x-5), yep

(2x-7) (x-5) = 0

set to zero

2x-7=0

2x=7

x=7/2

x-5=0

x=5

x=7/2 and 5