6(u+1)-9=4(u-1)2u

Solution for 6(u+1)-9=4(u-1)2u equation:

6(u+1)-9=4(u-1)2u

We move all terms to the left:

6(u+1)-9-(4(u-1)2u)=0

We multiply parentheses

6u-(4(u-1)2u)+6-9=0


We calculate terms in parentheses: -(4(u-1)2u), so:

4(u-1)2u

We multiply parentheses

8u^2-8u

Back to the equation:

-(8u^2-8u)


We add all the numbers together, and all the variables

6u-(8u^2-8u)-3=0

We get rid of parentheses

-8u^2+6u+8u-3=0

We add all the numbers together, and all the variables

-8u^2+14u-3=0

a = -8; b = 14; c = -3;
Δ = b2-4ac
Δ = 142-4·(-8)·(-3)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-10}{2*-8}=\frac{-24}{-16}
=1+1/2
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+10}{2*-8}=\frac{-4}{-16}
=1/4
$