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49-14x+x^{2}+41=x^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(7-x\right)^{2}.
90-14x+x^{2}=x^{2}
Add 49 and 41 to get 90.
90-14x+x^{2}-x^{2}=0
Subtract x^{2} from both sides.
90-14x=0
Combine x^{2} and -x^{2} to get 0.
-14x=-90
Subtract 90 from both sides. Anything subtracted from zero gives its negation.
x=\frac{-90}{-14}
Divide both sides by -14.
x=\frac{45}{7}
Reduce the fraction \frac{-90}{-14} to lowest terms by extracting and canceling out -2.