-3u(-2u+8)-9u=7(u-1)-2

Solution for -3u(-2u+8)-9u=7(u-1)-2 equation:

-3u(-2u+8)-9u=7(u-1)-2

We move all terms to the left:

-3u(-2u+8)-9u-(7(u-1)-2)=0

We add all the numbers together, and all the variables

-9u-3u(-2u+8)-(7(u-1)-2)=0

We multiply parentheses

6u^2-9u-24u-(7(u-1)-2)=0


We calculate terms in parentheses: -(7(u-1)-2), so:

7(u-1)-2

We multiply parentheses

7u-7-2

We add all the numbers together, and all the variables

7u-9

Back to the equation:

-(7u-9)


We add all the numbers together, and all the variables

6u^2-33u-(7u-9)=0

We get rid of parentheses

6u^2-33u-7u+9=0

We add all the numbers together, and all the variables

6u^2-40u+9=0

a = 6; b = -40; c = +9;
Δ = b2-4ac
Δ = -402-4·6·9
Δ = 1384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1384}=\sqrt{4*346}=\sqrt{4}*\sqrt{346}=2\sqrt{346}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{346}}{2*6}=\frac{40-2\sqrt{346}}{12}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{346}}{2*6}=\frac{40+2\sqrt{346}}{12}
$