(9+u)(2u-3)=0

Solution for (9+u)(2u-3)=0 equation:

(9+u)(2u-3)=0

We add all the numbers together, and all the variables

(u+9)(2u-3)=0

We multiply parentheses ..

(+2u^2-3u+18u-27)=0

We get rid of parentheses

2u^2-3u+18u-27=0

We add all the numbers together, and all the variables

2u^2+15u-27=0

a = 2; b = 15; c = -27;
Δ = b2-4ac
Δ = 152-4·2·(-27)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-21}{2*2}=\frac{-36}{4}
=-9
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+21}{2*2}=\frac{6}{4}
=1+1/2
$