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

Solution for (9+u)(4u-6)=0 equation:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+4u^2-6u+36u-54)=0

We get rid of parentheses

4u^2-6u+36u-54=0

We add all the numbers together, and all the variables

4u^2+30u-54=0

a = 4; b = 30; c = -54;
Δ = b2-4ac
Δ = 302-4·4·(-54)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-42}{2*4}=\frac{-72}{8}
=-9
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+42}{2*4}=\frac{12}{8}
=1+1/2
$