(u-4)(6u-7)=0

Solution for (u-4)(6u-7)=0 equation:

(u-4)(6u-7)=0

We multiply parentheses ..

(+6u^2-7u-24u+28)=0

We get rid of parentheses

6u^2-7u-24u+28=0

We add all the numbers together, and all the variables

6u^2-31u+28=0

a = 6; b = -31; c = +28;
Δ = b2-4ac
Δ = -312-4·6·28
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{-(-31)-17}{2*6}=\frac{14}{12}
=1+1/6
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+17}{2*6}=\frac{48}{12}
=4
$