(2u-1)(5u+1)=0

Solution for (2u-1)(5u+1)=0 equation:

(2u-1)(5u+1)=0

We multiply parentheses ..

(+10u^2+2u-5u-1)=0

We get rid of parentheses

10u^2+2u-5u-1=0

We add all the numbers together, and all the variables

10u^2-3u-1=0

a = 10; b = -3; c = -1;
Δ = b2-4ac
Δ = -32-4·10·(-1)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-7}{2*10}=\frac{-4}{20}
=-1/5
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+7}{2*10}=\frac{10}{20}
=1/2
$