-4u(u+2)=7u-6+2(2u+2)

Solution for -4u(u+2)=7u-6+2(2u+2) equation:

-4u(u+2)=7u-6+2(2u+2)

We move all terms to the left:

-4u(u+2)-(7u-6+2(2u+2))=0

We multiply parentheses

-4u^2-8u-(7u-6+2(2u+2))=0


We calculate terms in parentheses: -(7u-6+2(2u+2)), so:

7u-6+2(2u+2)

determiningTheFunctionDomain
7u+2(2u+2)-6

We multiply parentheses

7u+4u+4-6

We add all the numbers together, and all the variables

11u-2

Back to the equation:

-(11u-2)


We get rid of parentheses

-4u^2-8u-11u+2=0

We add all the numbers together, and all the variables

-4u^2-19u+2=0

a = -4; b = -19; c = +2;
Δ = b2-4ac
Δ = -192-4·(-4)·2
Δ = 393
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-\sqrt{393}}{2*-4}=\frac{19-\sqrt{393}}{-8}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{393}}{2*-4}=\frac{19+\sqrt{393}}{-8}
$