(3u-2)(2u-7)=0

Solution for (3u-2)(2u-7)=0 equation:

(3u-2)(2u-7)=0

We multiply parentheses ..

(+6u^2-21u-4u+14)=0

We get rid of parentheses

6u^2-21u-4u+14=0

We add all the numbers together, and all the variables

6u^2-25u+14=0

a = 6; b = -25; c = +14;
Δ = b2-4ac
Δ = -252-4·6·14
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-17}{2*6}=\frac{8}{12}
=2/3
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+17}{2*6}=\frac{42}{12}
=3+1/2
$