4(5x+1)=-11x(x+1)

Solution for 4(5x+1)=-11x(x+1) equation:

4(5x+1)=-11x(x+1)

We move all terms to the left:

4(5x+1)-(-11x(x+1))=0

We multiply parentheses

20x-(-11x(x+1))+4=0


We calculate terms in parentheses: -(-11x(x+1)), so:

-11x(x+1)

We multiply parentheses

-11x^2-11x

Back to the equation:

-(-11x^2-11x)


We get rid of parentheses

11x^2+11x+20x+4=0

We add all the numbers together, and all the variables

11x^2+31x+4=0

a = 11; b = 31; c = +4;
Δ = b2-4ac
Δ = 312-4·11·4
Δ = 785
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-\sqrt{785}}{2*11}=\frac{-31-\sqrt{785}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+\sqrt{785}}{2*11}=\frac{-31+\sqrt{785}}{22}
$