4(u+1)+5=6(u-1)u

Solution for 4(u+1)+5=6(u-1)u equation:

4(u+1)+5=6(u-1)u

We move all terms to the left:

4(u+1)+5-(6(u-1)u)=0

We multiply parentheses

4u-(6(u-1)u)+4+5=0


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

6(u-1)u

We multiply parentheses

6u^2-6u

Back to the equation:

-(6u^2-6u)


We add all the numbers together, and all the variables

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

We get rid of parentheses

-6u^2+4u+6u+9=0

We add all the numbers together, and all the variables

-6u^2+10u+9=0

a = -6; b = 10; c = +9;
Δ = b2-4ac
Δ = 102-4·(-6)·9
Δ = 316
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:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{79}}{2*-6}=\frac{-10-2\sqrt{79}}{-12}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{79}}{2*-6}=\frac{-10+2\sqrt{79}}{-12}
$