# How do you use the quadratic formula to solve x^2+5=4x?

May 3, 2015

$\frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$
can be used to find root solutions to quadratics in the form
$a {x}^{2} + b x + c = 0$

So first we need to convert the given equation into this form:
${x}^{2} + 5 = 4 x$

$\rightarrow {x}^{2} - 4 x + 5 = 0$

Solutions are
$x = \frac{- \left(- 4\right) \pm \sqrt{{\left(- 4\right)}^{2} - 4 \left(1\right) \left(5\right)}}{2 \left(1\right)}$

$x = 2 \pm \frac{\sqrt{\left(- 4\right)}}{2}$

Since the discriminant is negative
there are no Real value solutions to this equation
but within Complex numbers, the solution is
$x = 2 \pm i$