(7+u)(3u-1=0)

Solution for (7+u)(3u-1=0) equation:

(7+u)(3u-1=0)

We move all terms to the left:

(7+u)(3u-1-(0))=0

We add all the numbers together, and all the variables

(u+7)(3u-1)=0

We multiply parentheses ..

(+3u^2-1u+21u-7)=0

We get rid of parentheses

3u^2-1u+21u-7=0

We add all the numbers together, and all the variables

3u^2+20u-7=0

a = 3; b = 20; c = -7;
Δ = b2-4ac
Δ = 202-4·3·(-7)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-22}{2*3}=\frac{-42}{6}
=-7
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+22}{2*3}=\frac{2}{6}
=1/3
$