x^2+4x+5=3x^2+11x+1

Solution for x^2+4x+5=3x^2+11x+1 equation:

x^2+4x+5=3x^2+11x+1

We move all terms to the left:

x^2+4x+5-(3x^2+11x+1)=0

We get rid of parentheses

x^2-3x^2+4x-11x-1+5=0

We add all the numbers together, and all the variables

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

a = -2; b = -7; c = +4;
Δ = b2-4ac
Δ = -72-4·(-2)·4
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-9}{2*-2}=\frac{-2}{-4}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+9}{2*-2}=\frac{16}{-4}
=-4
$