Answer :

The quadratic is

[tex]x^2+35=5x[/tex]

Subtract 5x from both sides

[tex]\begin{gathered} x^2-5x+35=5x-5x \\ x^2-5x+35=0 \end{gathered}[/tex]

To solve it we will use the formula

[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]

a is the coefficient of x^2

b is the coefficient of x

c is the numerical term

Since a = 1, b = -5, c = 35

Then substitute them in the formula above

[tex]x=\frac{-(-5)\pm\sqrt[]{(-5)^2-4(1)(35)}}{2(1)}[/tex]

Simplify it

[tex]\begin{gathered} x=\frac{5\pm\sqrt[]{25-140}}{2} \\ x=\frac{5\pm\sqrt[]{-115}}{2} \end{gathered}[/tex]

since the square root of a -ve number is imaginary, then we will use i

[tex]\begin{gathered} x=\frac{5\pm\sqrt[]{115}.\sqrt[]{-1}}{2} \\ x=\frac{5\pm\sqrt[]{115}i}{2} \\ \sqrt[]{-1}=i \end{gathered}[/tex]

The solutions are

[tex]\mleft\lbrace\frac{5+\sqrt[]{115}i}{2},\frac{5-\sqrt[]{115}i}{2}\mright\rbrace[/tex]