34+4x=x^2

Solution for 34+4x=x^2 equation:

34+4x=x^2

We move all terms to the left:

34+4x-(x^2)=0

determiningTheFunctionDomain
-x^2+4x+34=0

We add all the numbers together, and all the variables

-1x^2+4x+34=0

a = -1; b = 4; c = +34;
Δ = b2-4ac
Δ = 42-4·(-1)·34
Δ = 152
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:

$\sqrt{\Delta}=\sqrt{152}=\sqrt{4*38}=\sqrt{4}*\sqrt{38}=2\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{38}}{2*-1}=\frac{-4-2\sqrt{38}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{38}}{2*-1}=\frac{-4+2\sqrt{38}}{-2}
$