-4u(u+1)=2(1-2u)-6

Solution for -4u(u+1)=2(1-2u)-6 equation:

-4u(u+1)=2(1-2u)-6

We move all terms to the left:

-4u(u+1)-(2(1-2u)-6)=0

We add all the numbers together, and all the variables

-4u(u+1)-(2(-2u+1)-6)=0

We multiply parentheses

-4u^2-4u-(2(-2u+1)-6)=0


We calculate terms in parentheses: -(2(-2u+1)-6), so:

2(-2u+1)-6

We multiply parentheses

-4u+2-6

We add all the numbers together, and all the variables

-4u-4

Back to the equation:

-(-4u-4)


We get rid of parentheses

-4u^2-4u+4u+4=0

We add all the numbers together, and all the variables

-4u^2+4=0

a = -4; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-4)·4
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8}{2*-4}=\frac{-8}{-8}
=1
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8}{2*-4}=\frac{8}{-8}
=-1
$