(6-u)(5u-8)=0

Solution for (6-u)(5u-8)=0 equation:

(6-u)(5u-8)=0

We add all the numbers together, and all the variables

(-1u+6)(5u-8)=0

We multiply parentheses ..

(-5u^2+8u+30u-48)=0

We get rid of parentheses

-5u^2+8u+30u-48=0

We add all the numbers together, and all the variables

-5u^2+38u-48=0

a = -5; b = 38; c = -48;
Δ = b2-4ac
Δ = 382-4·(-5)·(-48)
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{-(38)-22}{2*-5}=\frac{-60}{-10}
=+6
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+22}{2*-5}=\frac{-16}{-10}
=1+3/5
$