62x-8x+3=0 has no (real) solutions.
Perhaps the question should be:
2(32x)-(5+3x)+3=0. Let y=3x, then:
2y2-5-y+3=0,
2y2-y-2=0,
y2-y/2=1,
y2-y/2+1/16=17/16,
(y-¼)2=17/16,
y-¼=√17/4, y=¼±¼√17, y=1.28078 or -0.78078 approx.
Therefore 3x=1.28078 (the negative y is rejected because no power of 3 has a negative result).
xlog(3)=log(1.28078), x=log(1.28078)/log(3)=0.22525 approx.
Or is the question 2(32x)-5(3x)+3=0?
Let y=3x, then 2y2-5y+3=0=(y-1)(2y-3), so y=1 or 1.5.
3x=1, so x=0; or 3x=1.5, x=log(1.5)/log(3)=0.3691 approx.