4x+7=x^2

Solution for 4x+7=x^2 equation:

4x+7=x^2

We move all terms to the left:

4x+7-(x^2)=0

determiningTheFunctionDomain
-x^2+4x+7=0

We add all the numbers together, and all the variables

-1x^2+4x+7=0

a = -1; b = 4; c = +7;
Δ = b2-4ac
Δ = 42-4·(-1)·7
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{11}}{2*-1}=\frac{-4-2\sqrt{11}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{11}}{2*-1}=\frac{-4+2\sqrt{11}}{-2}
$