(5u-1)(6-u)=0

Solution for (5u-1)(6-u)=0 equation:

(5u-1)(6-u)=0

We add all the numbers together, and all the variables

(5u-1)(-1u+6)=0

We multiply parentheses ..

(-5u^2+30u+u-6)=0

We get rid of parentheses

-5u^2+30u+u-6=0

We add all the numbers together, and all the variables

-5u^2+31u-6=0

a = -5; b = 31; c = -6;
Δ = b2-4ac
Δ = 312-4·(-5)·(-6)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-29}{2*-5}=\frac{-60}{-10}
=+6
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+29}{2*-5}=\frac{-2}{-10}
=1/5
$