y^2-6y=-7
x^2=8x-41
(4x-1)(2x+6)=3x
45-t^2=0
(3x-6)^2=33
They want you to solve for the unknown variable. You need to rewrite the equation in quadratic form
ax^2 + bx + c = 0, first of all.
y^2 -6x = -7 can be rewritten
y^2 -6x +7 = 0
Use the quadratic formula to solve.
http://www.purplemath.com/modules/quadform.htm
y = [6 +/-sqrt(36-28)]/2
= 3 +/- sqrt2
You do the others; someone will check your work if you make the effort.