I think this is the right answer. I did the checking and I got it right. ^_^
Given: 2x^2-12x=15
2x^2-12x=15
X^2-6x=15/2
X^2-6x+9=15/2+9
(x-3)^2 = 33/2
(x-3)^2 = 33/2
x-3 =√33/√2
x-3 =(√33/√2)(√2/√2)
x-3 = ±√66/2
x-3= √66/2
x = √66/2 + 3
x = (6+√66)/2
x-3= - √66/2
x = - √66/2 + 3
x = (6-√66)/2
checking:
2x^2-12x=15
2[(6-√66)/2]^2 – 12[(6-√66)/2] = 15
2[(36-6√66-6√66+66)/4] – [6(6-√66)] = 15
2[(102-12√66)/4] – [36-6√66] = 15
2[6(17-2√66)/4] – [36-6√66] = 15
2[3(17-2√66)/2] – [36-6√66] = 15
3(17-2√66) – [36-6√66] = 15
51 – 6√66 -36+6√66 = 15
15 = 15
