y = (1+ (6(sqrt(2))/5)x-6
y = ( [ 1 + √72 ] / 5 ) x - 6
y^2 = ( [ 1 + √72 ]^2 / 25 ) x^2 - (12/5) [ 1 + √72 ] x + 36 =
( [ 73 + 2√72] / 25 ) x^2 - (12/5) [ 1 + √72 ] x + 36
Put this back into x^2 + y^2 = 36 for y^2
x^2 + ( [ 73 + 2√72] / 25 ) x^2 - (12/5) [ 1 + √72 ] x + 36 = 36
x^2 + ( [ 73 + 2√72] / 25 ) x^2 - (12/5) [ 1 + √72 ] x = 0 factor
x ( [ 1 + [ 73 + 2√72] / 25) ] x - (12/5) [ 1 + √72 ] ) = 0 set each factor to 0
x = 0 and
( [ 1 + ( [ 73 + 2√72] / 25) ] x - (12/5) [ 1 + √72 ] ) = 0
[ [25 + 73 + 2√72] / 25] x = [ 12 [ 1 + √72 ] ] / 5
[[ 98 + 2√72] / 25] x = [ 12 + 12 √72] / 5
[ (98 + 2√72) / 5] x = [ 12 + 12 √72]
x = 5* [ 12 + 12 √72] / (98 + 2√72) ≈ 4.9501
Here's the graph : https://www.desmos.com/calculator/wjjz1t33v1