4x2+2x=272.

Solution for 4x2+2x=272. equation:

4x^2+2x=272.

We move all terms to the left:

4x^2+2x-(272.)=0

We add all the numbers together, and all the variables

4x^2+2x-272=0

a = 4; b = 2; c = -272;
Δ = b2-4ac
Δ = 22-4·4·(-272)
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-66}{2*4}=\frac{-68}{8}
=-8+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+66}{2*4}=\frac{64}{8}
=8
$