Answer:
Given: The equation \(x^2=8-5x\)
we can write this as;
\(x^2+5x-8=0\)
The general equation of quadratic formula for \(ax^2+bx+c=0\) where a, b and c are constant ;
then the solution for this equation is given by;
\(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)
From the given equation;
we have a =1 , b =5 and c=-8
then, the solution of the given equation is;
\(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{-5\pm\sqrt{5^2-4(1)(-8)}}{2(1)}\)
or
\(x=\frac{-5\pm\sqrt{25+32}}{2}=\frac{-5\pm\sqrt{57}}{2}\)
therefore, the solution of the given equation is;
\(x=\frac{-5+\sqrt{57}}{2}\) and \(x=\frac{-5-\sqrt{57}}{2}\)
