4x+46=x^2=4x-18

Solution for 4x+46=x^2=4x-18 equation:

4x+46=x^2=4x-18

We move all terms to the left:

4x+46-(x^2)=0

determiningTheFunctionDomain
-x^2+4x+46=0

We add all the numbers together, and all the variables

-1x^2+4x+46=0

a = -1; b = 4; c = +46;
Δ = b2-4ac
Δ = 42-4·(-1)·46
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-10\sqrt{2}}{2*-1}=\frac{-4-10\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+10\sqrt{2}}{2*-1}=\frac{-4+10\sqrt{2}}{-2}
$