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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

4x^2+15x-4=0

a = 4; b = 15; c = -4;
Δ = b2-4ac
Δ = 152-4·4·(-4)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-17}{2*4}=\frac{-32}{8}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+17}{2*4}=\frac{2}{8}
=1/4
$