10(x-2)+19=(5x-1)(5x+1)

Solution for 10(x-2)+19=(5x-1)(5x+1) equation:

10(x-2)+19=(5x-1)(5x+1)

We move all terms to the left:

10(x-2)+19-((5x-1)(5x+1))=0

We use the square of the difference formula

25x^2+10(x-2)+1+19=0

We multiply parentheses

25x^2+10x-20+1+19=0

We add all the numbers together, and all the variables

25x^2+10x=0

a = 25; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·25·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*25}=\frac{-20}{50}
=-2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*25}=\frac{0}{50}
=0
$