The solution of equation $4+6+8+10+\cdots +x =270$ is 15. The solution of equation 
$4+6+8+10+\cdots +x =270$ 
is $x=15$. 
How can I prove it? 
I ve tried the geometric sequence but I cannot figure out the pattern.

$$4+6+8+10+\cdots +x=270\\ \frac { 4+x }{ 2 } \left( \frac { x-4 }{ 2 } +1 \right) =270\\ \frac { \left( 4+x \right)  }{ 2 } \frac { \left( x-2 \right)  }{ 2 } =270\\ \left( x-2 \right) \left( x+4 \right) =1080\\ { x }^{ 2 }+2x-1088=0\\ x=-1\pm \sqrt { 1089 } \\ x=32$$
