4x-12^2=x-x^2+4

Solution for 4x-12^2=x-x^2+4 equation:

4x-12^2=x-x^2+4

We move all terms to the left:

4x-12^2-(x-x^2+4)=0

We add all the numbers together, and all the variables

-(x-x^2+4)+4x-144=0

We get rid of parentheses

x^2-x+4x-4-144=0

We add all the numbers together, and all the variables

x^2+3x-148=0

a = 1; b = 3; c = -148;
Δ = b2-4ac
Δ = 32-4·1·(-148)
Δ = 601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{601}}{2*1}=\frac{-3-\sqrt{601}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{601}}{2*1}=\frac{-3+\sqrt{601}}{2}
$