2x+11=4x^2

Solution for 2x+11=4x^2 equation:

2x+11=4x^2

We move all terms to the left:

2x+11-(4x^2)=0

determiningTheFunctionDomain
-4x^2+2x+11=0

a = -4; b = 2; c = +11;
Δ = b2-4ac
Δ = 22-4·(-4)·11
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6\sqrt{5}}{2*-4}=\frac{-2-6\sqrt{5}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6\sqrt{5}}{2*-4}=\frac{-2+6\sqrt{5}}{-8}
$