23-x2-4x=0

Solution for 23-x2-4x=0 equation:

23-x2-4x=0

We add all the numbers together, and all the variables

-1x^2-4x+23=0

a = -1; b = -4; c = +23;
Δ = b2-4ac
Δ = -42-4·(-1)·23
Δ = 108
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-6\sqrt{3}}{2*-1}=\frac{4-6\sqrt{3}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+6\sqrt{3}}{2*-1}=\frac{4+6\sqrt{3}}{-2}
$