180=3×60 or (-3)×(-60), so if (for example) 7x+75=-3 and 11x+63=-60 we can find x, which must be exactly the same value from each equation.
7x=-78 and 11x=-123⇒x=-11.14 and -11.18 approx. These values are almost the same, so we would expect one solution to be around -11.
Expand the parentheses:
77x2+1266x+4725=180,
77x2+1266x+4545=0. Using the quadratic formula:
x=(-1266±√(1602756-1399860))/154,
x=(-1266±√202896)/154,
x=(-1266±450.4398)/154=-5.2958 or -11.1457 approx (close to -111/7 or -78/7).
We can see that one solution has x close to -11, as expected.
We can also use the iterative formula:
xn+1=xn-(77xn2+1266xn+4545)/(154xn+1266) where x0=-5:
x1=-5.2822..., x2=-5.2958..., x3=-5.295845551..., x4=-5.29584555131. So we have convergence to a solution x=-5.2958 (approx), as expected. The two solutions are x=-5.2958 and -11.1457 (approx).