122x+(4x^2)=264

Solution for 122x+(4x^2)=264 equation:

122x+(4x^2)=264

We move all terms to the left:

122x+(4x^2)-(264)=0

determiningTheFunctionDomain
4x^2+122x-264=0

a = 4; b = 122; c = -264;
Δ = b2-4ac
Δ = 1222-4·4·(-264)
Δ = 19108
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:

$\sqrt{\Delta}=\sqrt{19108}=\sqrt{4*4777}=\sqrt{4}*\sqrt{4777}=2\sqrt{4777}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(122)-2\sqrt{4777}}{2*4}=\frac{-122-2\sqrt{4777}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(122)+2\sqrt{4777}}{2*4}=\frac{-122+2\sqrt{4777}}{8}
$