Move right part of the equation to left part with negative sign.
The equation is transformed from x2+4=5x to −5x+(x2+4)=0 This equation is of the form
a*x^2 + b*x + c = 0
A quadratic equation can be solved using the discriminant. The roots of the quadratic equation: x1=2aD−b x2=2a−D−b where D = b^2 - 4*a*c - it is the discriminant. Because a=1 b=−5 c=4 , then
D = b^2 - 4 * a * c =
(-5)^2 - 4 * (1) * (4) = 9
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or x1=4 x2=1
Vieta's Theorem
it is reduced quadratic equation px+q+x2=0 where p=ab p=−5 q=ac q=4 Vieta Formulas x1+x2=−p x1x2=q x1+x2=5 x1x2=4