((11x)^2)-13x+1=-5x

Solution for ((11x)^2)-13x+1=-5x equation:

((11x)^2)-13x+1=-5x

We move all terms to the left:

((11x)^2)-13x+1-(-5x)=0

determiningTheFunctionDomain
11x^2-13x-(-5x)+1=0

We get rid of parentheses

11x^2-13x+5x+1=0

We add all the numbers together, and all the variables

11x^2-8x+1=0

a = 11; b = -8; c = +1;
Δ = b2-4ac
Δ = -82-4·11·1
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{5}}{2*11}=\frac{8-2\sqrt{5}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{5}}{2*11}=\frac{8+2\sqrt{5}}{22}
$